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All questions of Mensuration for SSS 1 Exam
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The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is- a)9.7 cm3
- b)77.6 cm3
- c)58.2 cm3
- d)19.4 cm3
Correct answer is option 'D'. Can you explain this answer?
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
a)
9.7 cm3
b)
77.6 cm3
c)
58.2 cm3
d)
19.4 cm3
|
Rajeev Malik answered |
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.
Edge of the cube = 4.2 cm
i.e 2r = 4.2
r = 4.2/2 = 2.1 cm
h = 4.2 cm
Volume of the cone = 1/3 * pi * r^2 * h
=> 1/3 * 22/7 * 2.1 * 2.1 * 4.2
=> 19.404 cm^3
Hence, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.
The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is - a)4.2
- b)2.1
- c)8.1
- d)1.05
Correct answer is option 'B'. Can you explain this answer?
The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
a)
4.2
b)
2.1
c)
8.1
d)
1.05
|
|
Abhi Prajapati answered |
Diameter of cone = edge of cube.
2r =4.1
r = 4.1/2
r = 2.1 cm
Hence radius of cone is equal to 2.1cm
2r =4.1
r = 4.1/2
r = 2.1 cm
Hence radius of cone is equal to 2.1cm
A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity is- a)5390.60 cm3
- b)5100 cm3
- c)5400 cm3
- d)5425.92 cm3
Correct answer is option 'D'. Can you explain this answer?
A container is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is 24 cm and the total height of the container is 16 cm. Its capacity is
a)
5390.60 cm3
b)
5100 cm3
c)
5400 cm3
d)
5425.92 cm3
|
Meghana shah answered |
To find the capacity of the container, we need to calculate the volume of the hemispherical bowl and the volume of the cylinder separately, and then add them together.
Given:
Diameter of the sphere = 24 cm
Total height of the container = 16 cm
**Calculating the Volume of the Hemispherical Bowl:**
The radius of the sphere (r) can be calculated by dividing the diameter by 2.
r = 24 cm / 2 = 12 cm
The volume of a hemisphere is given by the formula:
V_hemisphere = (2/3) * π * r^3
Substituting the value of r, we get:
V_hemisphere = (2/3) * π * 12^3
Calculating this value, we find:
V_hemisphere ≈ 3617.92 cm^3
**Calculating the Volume of the Cylinder:**
The height of the cylinder can be calculated by subtracting the radius of the sphere from the total height of the container.
Height of the cylinder = Total height of the container - Radius of the sphere
Height of the cylinder = 16 cm - 12 cm = 4 cm
The radius of the cylinder is the same as the radius of the sphere, which is 12 cm.
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Substituting the values of r and h, we get:
V_cylinder = π * 12^2 * 4
Calculating this value, we find:
V_cylinder ≈ 1809.28 cm^3
**Calculating the Total Capacity:**
The total capacity of the container is the sum of the volume of the hemisphere and the volume of the cylinder.
Total capacity = V_hemisphere + V_cylinder
Total capacity ≈ 3617.92 cm^3 + 1809.28 cm^3
Calculating this value, we find:
Total capacity ≈ 5427.20 cm^3
Rounding off to two decimal places, we get:
Total capacity ≈ 5425.92 cm^3
Therefore, the correct answer is option D) 5425.92 cm^3.
Given:
Diameter of the sphere = 24 cm
Total height of the container = 16 cm
**Calculating the Volume of the Hemispherical Bowl:**
The radius of the sphere (r) can be calculated by dividing the diameter by 2.
r = 24 cm / 2 = 12 cm
The volume of a hemisphere is given by the formula:
V_hemisphere = (2/3) * π * r^3
Substituting the value of r, we get:
V_hemisphere = (2/3) * π * 12^3
Calculating this value, we find:
V_hemisphere ≈ 3617.92 cm^3
**Calculating the Volume of the Cylinder:**
The height of the cylinder can be calculated by subtracting the radius of the sphere from the total height of the container.
Height of the cylinder = Total height of the container - Radius of the sphere
Height of the cylinder = 16 cm - 12 cm = 4 cm
The radius of the cylinder is the same as the radius of the sphere, which is 12 cm.
The volume of a cylinder is given by the formula:
V_cylinder = π * r^2 * h
Substituting the values of r and h, we get:
V_cylinder = π * 12^2 * 4
Calculating this value, we find:
V_cylinder ≈ 1809.28 cm^3
**Calculating the Total Capacity:**
The total capacity of the container is the sum of the volume of the hemisphere and the volume of the cylinder.
Total capacity = V_hemisphere + V_cylinder
Total capacity ≈ 3617.92 cm^3 + 1809.28 cm^3
Calculating this value, we find:
Total capacity ≈ 5427.20 cm^3
Rounding off to two decimal places, we get:
Total capacity ≈ 5425.92 cm^3
Therefore, the correct answer is option D) 5425.92 cm^3.
A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes is
- a)4: 5: 7
- b)3: 2: 1
- c)1: 2:3
- d)3: 1: 2
Correct answer is option 'D'. Can you explain this answer?
A cylinder, a cone and a hemisphere are of equal base and have the same height. The ratio of their volumes is
a)
4: 5: 7
b)
3: 2: 1
c)
1: 2:3
d)
3: 1: 2
|
Abhishek Kumar Pandey answered |
According to me, Option D is not the right answer.....
option B is the right answer.
I am sorry because I couldn't able to attach the solution...
solution:
let r be the radius and h be the height.
so, ratio of volume of cylinder,cone& hemisphere=
πr²h: 1/3πr²h:2/3πr³
(since h=r)
=> πr³:1/3πr³:2/3πr³
=>1:1/3:2/3
=>3:1:2
your explanation.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Two identical solid cube of side 5 cm are joined end to end. Then total surface area of the resulting cuboid is 300 cm2 .Reason : Total surface area of a cuboid is 2(lb + bh + lh)- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'D'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Two identical solid cube of side 5 cm are joined end to end. Then total surface area of the resulting cuboid is 300 cm2 .
Reason : Total surface area of a cuboid is 2(lb + bh + lh)
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
Radha Iyer answered |
When cubes are joined end to end, it will form a cuboid.
l = 2 x 5 = 10 cm , b = 5 cm
and h = 5 cm
Total surface area = 2(lb + bh + lh)
= 2(10 x 5 + 5 + 5 x 10 x 5)
= 2 x 125 = 250 cm2
A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumes- a)1:1:1
- b)2:3:1
- c)3 :1 :2
- d)1:2:3
Correct answer is option 'C'. Can you explain this answer?
A cylinder, a cone and a hemisphere have equal base and height. Find the ratio of their volumes
a)
1:1:1
b)
2:3:1
c)
3 :1 :2
d)
1:2:3
|
Nandini jain answered |
**Given**
- A cylinder, a cone, and a hemisphere have equal base and height.
**To Find**
- The ratio of their volumes.
**Solution**
Let's assume the height and base radius of each shape to be 'h' and 'r', respectively.
**Volume of a Cylinder**
The volume of a cylinder is given by the formula:
Vcylinder = πr^2h
**Volume of a Cone**
The volume of a cone is given by the formula:
Vcone = (1/3)πr^2h
**Volume of a Hemisphere**
The volume of a hemisphere is given by the formula:
Vhemisphere = (2/3)πr^3
**Given Conditions**
- The base radius and height of the cylinder, cone, and hemisphere are equal.
- So, r = h for all three shapes.
**Substituting Values**
Substituting r = h in the volume formulas for each shape, we get:
Vcylinder = πr^2h = πh^2h = πh^3
Vcone = (1/3)πr^2h = (1/3)πh^2h = (1/3)πh^3
Vhemisphere = (2/3)πr^3 = (2/3)πh^3
**Comparing Volumes**
The ratio of the volumes of the cylinder, cone, and hemisphere can be found by dividing each volume by the volume of the cylinder (since the cylinder has the largest volume):
Ratio = (Vcylinder : Vcone : Vhemisphere) / Vcylinder
= (πh^3 : (1/3)πh^3 : (2/3)πh^3) / πh^3
= 1 : (1/3) : (2/3)
= 3 : 1 : 2
Therefore, the ratio of their volumes is 3 : 1 : 2. The correct answer is option 'C'.
- A cylinder, a cone, and a hemisphere have equal base and height.
**To Find**
- The ratio of their volumes.
**Solution**
Let's assume the height and base radius of each shape to be 'h' and 'r', respectively.
**Volume of a Cylinder**
The volume of a cylinder is given by the formula:
Vcylinder = πr^2h
**Volume of a Cone**
The volume of a cone is given by the formula:
Vcone = (1/3)πr^2h
**Volume of a Hemisphere**
The volume of a hemisphere is given by the formula:
Vhemisphere = (2/3)πr^3
**Given Conditions**
- The base radius and height of the cylinder, cone, and hemisphere are equal.
- So, r = h for all three shapes.
**Substituting Values**
Substituting r = h in the volume formulas for each shape, we get:
Vcylinder = πr^2h = πh^2h = πh^3
Vcone = (1/3)πr^2h = (1/3)πh^2h = (1/3)πh^3
Vhemisphere = (2/3)πr^3 = (2/3)πh^3
**Comparing Volumes**
The ratio of the volumes of the cylinder, cone, and hemisphere can be found by dividing each volume by the volume of the cylinder (since the cylinder has the largest volume):
Ratio = (Vcylinder : Vcone : Vhemisphere) / Vcylinder
= (πh^3 : (1/3)πh^3 : (2/3)πh^3) / πh^3
= 1 : (1/3) : (2/3)
= 3 : 1 : 2
Therefore, the ratio of their volumes is 3 : 1 : 2. The correct answer is option 'C'.
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.- a)200 cm3
- b)600 cm3
- c)550 cm3
- d)616 cm3
Correct answer is option 'D'. Can you explain this answer?
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.
a)
200 cm3
b)
600 cm3
c)
550 cm3
d)
616 cm3
|
|
Rajeev Chavan answered |
Given:
Radius of cylindrical tub, r = 5 cm
Length of cylindrical tub, l = 9.8 cm
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
To find: Volume of the water left in the tub
Approach:
First, we find the total volume of the cylindrical tub.
Then, we find the volume of the solid (cone mounted on a hemisphere) that is immersed in the tub.
Finally, we subtract the volume of the solid from the total volume of the tub to get the volume of the water left in the tub.
Calculation:
1. Volume of the cylindrical tub
Given,
Radius of the cylindrical tub, r = 5 cm
Length of the cylindrical tub, l = 9.8 cm
The formula for the volume of a cylinder is:
V_cylinder = πr^2l
Substituting the given values, we get:
V_cylinder = π(5)^2(9.8) = 245π cm^3
2. Volume of the solid (cone mounted on a hemisphere)
Given,
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
The solid consists of a cone mounted on a hemisphere. We can find the volume of the solid by adding the volumes of the cone and the hemisphere.
The formula for the volume of a cone is:
V_cone = 1/3πr^2h
Substituting the given values, we get:
V_cone = 1/3π(3.5)^2(5) = 61.25π/3 cm^3
The formula for the volume of a hemisphere is:
V_hemisphere = 2/3πR^3
Substituting the given values, we get:
V_hemisphere = 2/3π(3.5)^3 = 42.875π/3 cm^3
Therefore, the volume of the solid is:
V_solid = V_cone + V_hemisphere = 61.25π/3 + 42.875π/3 = 104.125π/3 cm^3
3. Volume of the water left in the tub
The volume of the water left in the tub is the total volume of the cylindrical tub minus the volume of the solid that is immersed in the tub.
V_water = V_cylinder - V_solid
V_water = 245π - 104.125π/3
V_water = 735/3π - 104.125/3π
V_water = (735 - 104.125)/3π
V_water = 216.875/3π cm^3
V_water = 216.875/3 × 3.14
V_water = 616.06 cm^3
Therefore, the volume of the water left in the tub is 616.06 cm^3 (approximately).
Hence, the correct option is (d) 616 cm^3.
Radius of cylindrical tub, r = 5 cm
Length of cylindrical tub, l = 9.8 cm
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
To find: Volume of the water left in the tub
Approach:
First, we find the total volume of the cylindrical tub.
Then, we find the volume of the solid (cone mounted on a hemisphere) that is immersed in the tub.
Finally, we subtract the volume of the solid from the total volume of the tub to get the volume of the water left in the tub.
Calculation:
1. Volume of the cylindrical tub
Given,
Radius of the cylindrical tub, r = 5 cm
Length of the cylindrical tub, l = 9.8 cm
The formula for the volume of a cylinder is:
V_cylinder = πr^2l
Substituting the given values, we get:
V_cylinder = π(5)^2(9.8) = 245π cm^3
2. Volume of the solid (cone mounted on a hemisphere)
Given,
Radius of hemisphere, R = 3.5 cm
Height of cone outside the hemisphere, h = 5 cm
The solid consists of a cone mounted on a hemisphere. We can find the volume of the solid by adding the volumes of the cone and the hemisphere.
The formula for the volume of a cone is:
V_cone = 1/3πr^2h
Substituting the given values, we get:
V_cone = 1/3π(3.5)^2(5) = 61.25π/3 cm^3
The formula for the volume of a hemisphere is:
V_hemisphere = 2/3πR^3
Substituting the given values, we get:
V_hemisphere = 2/3π(3.5)^3 = 42.875π/3 cm^3
Therefore, the volume of the solid is:
V_solid = V_cone + V_hemisphere = 61.25π/3 + 42.875π/3 = 104.125π/3 cm^3
3. Volume of the water left in the tub
The volume of the water left in the tub is the total volume of the cylindrical tub minus the volume of the solid that is immersed in the tub.
V_water = V_cylinder - V_solid
V_water = 245π - 104.125π/3
V_water = 735/3π - 104.125/3π
V_water = (735 - 104.125)/3π
V_water = 216.875/3π cm^3
V_water = 216.875/3 × 3.14
V_water = 616.06 cm^3
Therefore, the volume of the water left in the tub is 616.06 cm^3 (approximately).
Hence, the correct option is (d) 616 cm^3.
A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be- a)6: 7
- b)4: 3
- c)3: 5
- d)5: 3
Correct answer is option 'C'. Can you explain this answer?
A cone and a cylinder have their heights in the ratio 4: 5 and their diameters are in the ratio 3: 2. The ratio of their volumes will be
a)
6: 7
b)
4: 3
c)
3: 5
d)
5: 3
|
Ananya Das answered |
Height of cone =4x
Height of cylinder=5x
Diameter of cone=3y
Diameter of cylinder=2y
Volume of cone=
Volume of cylinder= πr2h=y2*5x
Height of cylinder=5x
Diameter of cone=3y
Diameter of cylinder=2y
Volume of cone=
Volume of cylinder= πr2h=y2*5x
A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be- a)250 cm3
- b)200 cm3
- c)300 cm3
- d)218 cm3
Correct answer is option 'D'. Can you explain this answer?
A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be
a)
250 cm3
b)
200 cm3
c)
300 cm3
d)
218 cm3
|
|
Cat Warior answered |
D
A cylinder and a cone are of same base radius and of same height. The ratio of the volume of cylinder to that of the cone is:- a)1:2
- b)2:3
- c)3:1
- d)1:3
Correct answer is option 'C'. Can you explain this answer?
A cylinder and a cone are of same base radius and of same height. The ratio of the volume of cylinder to that of the cone is:
a)
1:2
b)
2:3
c)
3:1
d)
1:3
|
Pooja Shah answered |
We have radius of cylinder and cone = r
Height of cone and cylinder = h
Volume of cone =
Volume of cylinder = πr2h
Height of cone and cylinder = h
Volume of cone =
Volume of cylinder = πr2h
A cubical ice cream brick of edge 22 cm is to be distributed among some children by filling ice cream cones of radius 2 cm and height 7 cm upto its brim. How many children will get the ice cream cones?- a)163
- b)263
- c)363
- d)463
Correct answer is option 'C'. Can you explain this answer?
A cubical ice cream brick of edge 22 cm is to be distributed among some children by filling ice cream cones of radius 2 cm and height 7 cm upto its brim. How many children will get the ice cream cones?
a)
163
b)
263
c)
363
d)
463
|
|
Nature Lover answered |
A cylindrical vessel of diameter 42 cm and height 40 cm contains water up to a depth of 16 cm. Now a solid iron cylinder, with diameter 14 cm and height 32 cm is placed upright in the cylindrical vessel. The volume of the water required to just submerge the solid cylinder will be- a)17, 248 cm3
- b)14, 000 cm3
- c)15, 600 cm3
- d)16, 045 cm3
Correct answer is option 'A'. Can you explain this answer?
A cylindrical vessel of diameter 42 cm and height 40 cm contains water up to a depth of 16 cm. Now a solid iron cylinder, with diameter 14 cm and height 32 cm is placed upright in the cylindrical vessel. The volume of the water required to just submerge the solid cylinder will be
a)
17, 248 cm3
b)
14, 000 cm3
c)
15, 600 cm3
d)
16, 045 cm3
|
Tanishka Gupta answered |
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): A solid iron is in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere. Then the radius of sphere will be 21 cm.Reason (R): Volume of cylinder = πr2h, r is the radius of the cylinder and h is the height of the cylinder.- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'B'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): A solid iron is in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere. Then the radius of sphere will be 21 cm.
Reason (R): Volume of cylinder = πr2h, r is the radius of the cylinder and h is the height of the cylinder.
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
Gopal Saha answered |
A: A solid iron is in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm is melted to form a solid sphere. Then the radius of sphere will be 21 cm.
R: Volume of cylinder = πr2h, r is the radius of the cylinder and h is the height of the cylinder.
To solve this problem, we need to calculate the volume of the cuboid and the volume of the sphere and then compare them.
Volume of the cuboid:
Given dimensions of the cuboid are 49 cm × 33 cm × 24 cm.
Volume of cuboid = length × breadth × height
= 49 cm × 33 cm × 24 cm
= 38712 cm³
Volume of the sphere:
Let the radius of the sphere be 'R'.
Volume of sphere = (4/3)πR³
According to the given information, the solid iron is melted to form a solid sphere. This means that the volume of the sphere will be equal to the volume of the cuboid.
Therefore,
(4/3)πR³ = 38712 cm³
Now, we can solve this equation to find the value of 'R' (radius of the sphere).
Solving the equation:
(4/3)πR³ = 38712 cm³
R³ = (38712 cm³ × 3) / (4π)
R³ = 29034 cm³
R = ∛(29034 cm³)
R ≈ 31.11 cm
The radius of the sphere is approximately 31.11 cm, which is not equal to 21 cm. Therefore, the given statement of assertion is false.
Conclusion:
The statement of reason is correct as it provides the formula to calculate the volume of the cylinder. However, the statement of assertion is false as the radius of the sphere is not 21 cm, but approximately 31.11 cm. Hence, option B is the correct answer.
R: Volume of cylinder = πr2h, r is the radius of the cylinder and h is the height of the cylinder.
To solve this problem, we need to calculate the volume of the cuboid and the volume of the sphere and then compare them.
Volume of the cuboid:
Given dimensions of the cuboid are 49 cm × 33 cm × 24 cm.
Volume of cuboid = length × breadth × height
= 49 cm × 33 cm × 24 cm
= 38712 cm³
Volume of the sphere:
Let the radius of the sphere be 'R'.
Volume of sphere = (4/3)πR³
According to the given information, the solid iron is melted to form a solid sphere. This means that the volume of the sphere will be equal to the volume of the cuboid.
Therefore,
(4/3)πR³ = 38712 cm³
Now, we can solve this equation to find the value of 'R' (radius of the sphere).
Solving the equation:
(4/3)πR³ = 38712 cm³
R³ = (38712 cm³ × 3) / (4π)
R³ = 29034 cm³
R = ∛(29034 cm³)
R ≈ 31.11 cm
The radius of the sphere is approximately 31.11 cm, which is not equal to 21 cm. Therefore, the given statement of assertion is false.
Conclusion:
The statement of reason is correct as it provides the formula to calculate the volume of the cylinder. However, the statement of assertion is false as the radius of the sphere is not 21 cm, but approximately 31.11 cm. Hence, option B is the correct answer.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm2 .Reason : If r be the radius and h be the height of the cylinder, then total surface area = (2prh +2pr2).- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'A'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : Total surface area of the cylinder having radius of the base 14 cm and height 30 cm is 3872 cm2 .
Reason : If r be the radius and h be the height of the cylinder, then total surface area = (2prh +2pr2).
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Rohit Sharma answered |
Total surface area = 2prh +2pr2
= 2p r (h + r)
= 3872 cm2
In a swimming pool measuring 90 m x 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m3, then rise in water level is- a)27.33 cm
- b)30 cm
- c)31.33 cm
- d)33.33 cm
Correct answer is option 'D'. Can you explain this answer?
In a swimming pool measuring 90 m x 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m3, then rise in water level is
a)
27.33 cm
b)
30 cm
c)
31.33 cm
d)
33.33 cm
|
|
Anisha kapoor answered |
Volume of water displaced = 150 x 8 = 1200 m3
⇒ 90 x 40 x h = 1200
⇒
⇒ 90 x 40 x h = 1200
⇒
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm respectively. The curved surface area of the bucket is - a)4955 cm2
- b)4952 cm2
- c)4951 cm2
- d)4950 cm2
Correct answer is option 'D'. Can you explain this answer?
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm respectively. The curved surface area of the bucket is
a)
4955 cm2
b)
4952 cm2
c)
4951 cm2
d)
4950 cm2
|
|
Sanjay Jha answered |
Given
l= 45cm
r1 =28cm
r2= 7cm
curved surface area of bucket is 22/7(r1+r2) 45
= 22/7(28cm + 7cm ) 45
=22/7+35*45= 4950cmsq
l= 45cm
r1 =28cm
r2= 7cm
curved surface area of bucket is 22/7(r1+r2) 45
= 22/7(28cm + 7cm ) 45
=22/7+35*45= 4950cmsq
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed tha 1/8 space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is- a)142244
- b)142344
- c)142444
- d)142544
Correct answer is option 'A'. Can you explain this answer?
A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed tha 1/8 space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is
a)
142244
b)
142344
c)
142444
d)
142544
|
|
Rising Star answered |
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The Volume and Surface Area of a sphere are related to each other by radius.
Reason (R): Relation between Surface Area S and Volume V is S3 = 36πV2.
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Anita Menon answered |
Volume of sphere = 
⇒ 
⇒ 
⇒ 
Also, S = 4πr2
⇒ 
⇒ 
which proves that assertion is correct.
which proves that assertion is correct.Therefore, Both A and R are true and R is the correct explanation for A.
A mason constructs a wall of dimensions 270 cm x 300 cm x 350 cm with the bricks each of size 22.5 cm x 11.25 cm x 8.75 cm and it is assumed that 1/8 space is covered by the mortar.
Then the number of bricks used to construct the wall is- a)11100 cm
- b)11200 cm
- c)11000 cm
- d)11300 cm
Correct answer is option 'B'. Can you explain this answer?
A mason constructs a wall of dimensions 270 cm x 300 cm x 350 cm with the bricks each of size 22.5 cm x 11.25 cm x 8.75 cm and it is assumed that 1/8 space is covered by the mortar.
Then the number of bricks used to construct the wall is
Then the number of bricks used to construct the wall is
a)
11100 cm
b)
11200 cm
c)
11000 cm
d)
11300 cm
|
|
Poonam Rani answered |
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'D'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If the radius of a cone is halved and volume is not changed, then height remains same.
Reason : If the radius of a cone is halved and volume is not changed then height must become four times of the original height.
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Rohit Sharma answered |
As
Volume of a hollow right circular cylinder is- a)πr2h (R2 + r2)
- b)πr2h (R2 – r2)
- c)πrh (R2 – r2)
- d)πh (R2 – r2)
Correct answer is option 'D'. Can you explain this answer?
Volume of a hollow right circular cylinder is
a)
πr2h (R2 + r2)
b)
πr2h (R2 – r2)
c)
πrh (R2 – r2)
d)
πh (R2 – r2)
|
Ritu gupta answered |
Πr²h - πr₁²h
where r is the outer radius, r₁ is the inner radius, and h is the height of the cylinder.
where r is the outer radius, r₁ is the inner radius, and h is the height of the cylinder.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): The radii of two cone are in the ratio 2 : 3 and their volumes in the ratio 1 : 3. Then ratio of their heights is 3 : 2.Reason (R): Volume of Cone = 
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'D'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The radii of two cone are in the ratio 2 : 3 and their volumes in the ratio 1 : 3. Then ratio of their heights is 3 : 2.
Reason (R): Volume of Cone =
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Aditya Shah answered |
Let V1, V2 are the volumes of the two cones.
R and r be the radii of the two cones.
H and h be the heights of the two cones.
⇒ 
⇒ 
⇒ 
⇒ 
which proves that assertion is wrong.
which proves that assertion is wrong.Therefore, A is false but R is true.
A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4 cm. The radius of the base of the cylinder will be- a)4 cm
- b)2 cm
- c)5 cm
- d)8 cm
Correct answer is option 'A'. Can you explain this answer?
A cylinder whose height is two thirds of its diameter has the same volume as a sphere of radius 4 cm. The radius of the base of the cylinder will be
a)
4 cm
b)
2 cm
c)
5 cm
d)
8 cm
|
Animesh shah answered |
To solve this problem, we can use the formulas for the volume of a cylinder and the volume of a sphere. Let's break down the solution into steps:
Given information:
- The height of the cylinder is two-thirds of its diameter
- The volume of the cylinder is equal to the volume of a sphere with a radius of 4 cm
Step 1: Calculate the volume of the sphere
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since the radius of the sphere is given as 4 cm, we can substitute this value into the formula:
V_sphere = (4/3)π(4^3)
V_sphere = (4/3)π(64)
V_sphere = (4/3)(3.14)(64)
V_sphere ≈ 268.08 cm^3
Step 2: Set up the equation for the volume of the cylinder
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. We are given that the height of the cylinder is two-thirds of its diameter. Since the diameter is twice the radius, we can write the height as h = (2/3)(2r) = (4/3)r. Substituting these values into the formula, we get:
V_cylinder = πr^2(4/3)r
V_cylinder = (4/3)πr^3
Step 3: Equate the volumes of the cylinder and the sphere
Since the volume of the cylinder is equal to the volume of the sphere, we can set up the equation:
(4/3)πr^3 = 268.08
Dividing both sides by (4/3)π, we get:
r^3 = 268.08 / (4/3)π
r^3 = 201.06 / π
Taking the cube root of both sides, we find:
r = (201.06/π)^(1/3)
r ≈ 4 cm
Therefore, the radius of the base of the cylinder is approximately 4 cm, which corresponds to option A.
Given information:
- The height of the cylinder is two-thirds of its diameter
- The volume of the cylinder is equal to the volume of a sphere with a radius of 4 cm
Step 1: Calculate the volume of the sphere
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius. Since the radius of the sphere is given as 4 cm, we can substitute this value into the formula:
V_sphere = (4/3)π(4^3)
V_sphere = (4/3)π(64)
V_sphere = (4/3)(3.14)(64)
V_sphere ≈ 268.08 cm^3
Step 2: Set up the equation for the volume of the cylinder
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. We are given that the height of the cylinder is two-thirds of its diameter. Since the diameter is twice the radius, we can write the height as h = (2/3)(2r) = (4/3)r. Substituting these values into the formula, we get:
V_cylinder = πr^2(4/3)r
V_cylinder = (4/3)πr^3
Step 3: Equate the volumes of the cylinder and the sphere
Since the volume of the cylinder is equal to the volume of the sphere, we can set up the equation:
(4/3)πr^3 = 268.08
Dividing both sides by (4/3)π, we get:
r^3 = 268.08 / (4/3)π
r^3 = 201.06 / π
Taking the cube root of both sides, we find:
r = (201.06/π)^(1/3)
r ≈ 4 cm
Therefore, the radius of the base of the cylinder is approximately 4 cm, which corresponds to option A.
A shuttle cock used for playing badminton has the shape of the combination of- a)a cylinder and a sphere
- b)a cylinder and a hemisphere
- c)a sphere and a cone
- d)frustum of a cone and a hemisphere
Correct answer is option 'D'. Can you explain this answer?
A shuttle cock used for playing badminton has the shape of the combination of
a)
a cylinder and a sphere
b)
a cylinder and a hemisphere
c)
a sphere and a cone
d)
frustum of a cone and a hemisphere
|
|
Vaibhav Roy answered |
Explanation:
The shuttlecock used in playing badminton has a unique shape that helps it to move swiftly through the air. The shape of a shuttlecock is the combination of two 3D shapes - a frustum of a cone and a hemisphere.
Frustum of a Cone: The top part of the shuttlecock is shaped like the frustum of a cone. A frustum of a cone is a 3D shape that is formed when the top part of a cone is cut off parallel to the base. The frustum of a cone has two circular bases, one larger than the other, and a curved surface.
Hemisphere: The bottom part of the shuttlecock is shaped like a hemisphere. A hemisphere is a 3D shape that is formed when a sphere is cut in half. A hemisphere has a curved surface and a circular base.
Combination of Frustum of a Cone and Hemisphere: The shuttlecock is made by joining the frustum of a cone and hemisphere at their circular bases. The frustum of a cone forms the top part of the shuttlecock, while the hemisphere forms the bottom part.
The frustum of a cone and hemisphere are combined to create the unique shape of the shuttlecock. This shape helps the shuttlecock to move swiftly through the air and change direction easily, making it perfect for playing badminton.
The shuttlecock used in playing badminton has a unique shape that helps it to move swiftly through the air. The shape of a shuttlecock is the combination of two 3D shapes - a frustum of a cone and a hemisphere.
Frustum of a Cone: The top part of the shuttlecock is shaped like the frustum of a cone. A frustum of a cone is a 3D shape that is formed when the top part of a cone is cut off parallel to the base. The frustum of a cone has two circular bases, one larger than the other, and a curved surface.
Hemisphere: The bottom part of the shuttlecock is shaped like a hemisphere. A hemisphere is a 3D shape that is formed when a sphere is cut in half. A hemisphere has a curved surface and a circular base.
Combination of Frustum of a Cone and Hemisphere: The shuttlecock is made by joining the frustum of a cone and hemisphere at their circular bases. The frustum of a cone forms the top part of the shuttlecock, while the hemisphere forms the bottom part.
The frustum of a cone and hemisphere are combined to create the unique shape of the shuttlecock. This shape helps the shuttlecock to move swiftly through the air and change direction easily, making it perfect for playing badminton.
A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere of diameter- a)r cm
- b)2r cm
- c)h cm
- d)2h cm
Correct answer is option 'B'. Can you explain this answer?
A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere of diameter
a)
r cm
b)
2r cm
c)
h cm
d)
2h cm
|
|
Avantika nair answered |
The volume of a right circular cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
The total surface area of a right circular cylinder is given by the formula A = 2πrh + 2πr^2.
The lateral surface area of a right circular cylinder is given by the formula A = 2πrh.
The curved surface area of a right circular cylinder is given by the formula A = 2πrh.
The total surface area of a right circular cylinder is given by the formula A = 2πrh + 2πr^2.
The lateral surface area of a right circular cylinder is given by the formula A = 2πrh.
The curved surface area of a right circular cylinder is given by the formula A = 2πrh.
During conversion of a solid from one shape to another, the volume of the new shape will- a)increase
- b)decrease
- c)remain unaltered
- d)be doubled
Correct answer is option 'C'. Can you explain this answer?
During conversion of a solid from one shape to another, the volume of the new shape will
a)
increase
b)
decrease
c)
remain unaltered
d)
be doubled
|
|
Sarangi sharma answered |
Introduction:
When a solid undergoes a shape transformation, such as stretching, bending, or compressing, the volume of the new shape can change. This change in volume depends on the nature of the transformation and the properties of the material.
Explanation:
The volume of a solid is a measure of the amount of space it occupies. It is calculated by multiplying the area of the base of the solid by its height. When a solid undergoes a shape transformation, the base and height of the solid may change, resulting in a change in volume.
Example:
Let's consider the example of a cylindrical solid being transformed into a cone. The cylindrical solid has a circular base and a constant height. As the shape transforms into a cone, the base of the solid changes from a circle to a smaller circle, while the height remains the same.
Effect on volume:
When the base of the solid changes, the area of the base also changes. Since the volume of a solid is directly proportional to the base area, any change in the base area will result in a change in volume.
In this specific example, as the cylindrical solid transforms into a cone, the base area decreases since the radius of the base decreases. However, the height remains the same. As a result, the volume of the cone will be less than the volume of the cylindrical solid.
Conclusion:
In general, during the conversion of a solid from one shape to another, the volume of the new shape can either increase or decrease depending on the specific transformation. However, in some cases, such as when the height remains constant and only the base area changes, the volume of the new shape will remain unaltered. Therefore, the correct answer is option 'C' - the volume will remain unaltered.
When a solid undergoes a shape transformation, such as stretching, bending, or compressing, the volume of the new shape can change. This change in volume depends on the nature of the transformation and the properties of the material.
Explanation:
The volume of a solid is a measure of the amount of space it occupies. It is calculated by multiplying the area of the base of the solid by its height. When a solid undergoes a shape transformation, the base and height of the solid may change, resulting in a change in volume.
Example:
Let's consider the example of a cylindrical solid being transformed into a cone. The cylindrical solid has a circular base and a constant height. As the shape transforms into a cone, the base of the solid changes from a circle to a smaller circle, while the height remains the same.
Effect on volume:
When the base of the solid changes, the area of the base also changes. Since the volume of a solid is directly proportional to the base area, any change in the base area will result in a change in volume.
In this specific example, as the cylindrical solid transforms into a cone, the base area decreases since the radius of the base decreases. However, the height remains the same. As a result, the volume of the cone will be less than the volume of the cylindrical solid.
Conclusion:
In general, during the conversion of a solid from one shape to another, the volume of the new shape can either increase or decrease depending on the specific transformation. However, in some cases, such as when the height remains constant and only the base area changes, the volume of the new shape will remain unaltered. Therefore, the correct answer is option 'C' - the volume will remain unaltered.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.Reason : If r be the radius and h the slant height of the cone, then slant height = 
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'D'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If the height of a cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.
Reason : If r be the radius and h the slant height of the cone, then slant height =
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Avinash Patel answered |
Assertion (A) is false but reason (R) is true.
Slant height = 
The radii of two right circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 4. The ratio of their volumes will be- a)4: 3
- b)6: 7
- c)5: 9
- d)2: 3
Correct answer is option 'C'. Can you explain this answer?
The radii of two right circular cylinders are in the ratio 2: 3 and their heights are in the ratio 5: 4. The ratio of their volumes will be
a)
4: 3
b)
6: 7
c)
5: 9
d)
2: 3
|
|
Naveen Gupta answered |
Ratio of Radii:
Let the radii of the two cylinders be 2x and 3x.
Ratio of Heights:
Let the heights of the two cylinders be 5y and 4y.
Volume of a Cylinder:
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Finding the Volumes:
The volume of the first cylinder with radius 2x and height 5y is V₁ = π(2x)²(5y) = 20πx²y.
The volume of the second cylinder with radius 3x and height 4y is V₂ = π(3x)²(4y) = 36πx²y.
Ratio of Volumes:
The ratio of the volumes of the two cylinders is given by V₁ : V₂.
Substituting the values, we get V₁ : V₂ = 20πx²y : 36πx²y.
Simplifying, we get V₁ : V₂ = 5x²y : 9x²y.
Dividing both sides by x²y, we get V₁ : V₂ = 5 : 9.
Therefore, the ratio of the volumes of the two cylinders is 5 : 9, which corresponds to option C.
Let the radii of the two cylinders be 2x and 3x.
Ratio of Heights:
Let the heights of the two cylinders be 5y and 4y.
Volume of a Cylinder:
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Finding the Volumes:
The volume of the first cylinder with radius 2x and height 5y is V₁ = π(2x)²(5y) = 20πx²y.
The volume of the second cylinder with radius 3x and height 4y is V₂ = π(3x)²(4y) = 36πx²y.
Ratio of Volumes:
The ratio of the volumes of the two cylinders is given by V₁ : V₂.
Substituting the values, we get V₁ : V₂ = 20πx²y : 36πx²y.
Simplifying, we get V₁ : V₂ = 5x²y : 9x²y.
Dividing both sides by x²y, we get V₁ : V₂ = 5 : 9.
Therefore, the ratio of the volumes of the two cylinders is 5 : 9, which corresponds to option C.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): There are 1000 balls of diameter 0.6 cm which can be formed by melting a solid sphere of radius 3 cm.Reason (R):Number of spherical balls = (Volume of Bigger solid sphere)/(Volume of 1 spherical ball)- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): There are 1000 balls of diameter 0.6 cm which can be formed by melting a solid sphere of radius 3 cm.
Reason (R):Number of spherical balls = (Volume of Bigger solid sphere)/(Volume of 1 spherical ball)
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Rohit Sharma answered |
Radius of Ball = 0.3 cm and radius of solid sphere = 3 cm Volume of solid sphere = n × volume of 1 ball here n represents number of balls
Which proves both Assertion and reason are true.
Therefore, Both A and R are true and R is the correct explanation for A.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If a ball is in the shape of a sphere has a surface area of 221.76cm2 , then its diameter is 8.4 cm.Reason : If the radius of the sphere be r , then surface area, S = 4p r2 , i.e. 
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'A'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If a ball is in the shape of a sphere has a surface area of 221.76cm2 , then its diameter is 8.4 cm.
Reason : If the radius of the sphere be r , then surface area, S = 4p r2 , i.e.
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Vivek Rana answered |
Given, surface area of sphere = 221.76cm2
We know, surface area of sphere = 4πr2
⇒ 4(π)r2 = 221.76
⇒ r2 = 7/22 × 221.76 × 1/4 = 7 × (10.08) × 1/4
⇒ r = 4.2cm
Then, diameter equals 2r = 2 × 4.2 = 8.4 cm, which is true and reason is also correct.
Moreover reason is the correct explanation of assertion.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the height of the cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.Reason (R): If r be the radius of the cone and h be the height of the cone, then slant height = 
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'D'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If the height of the cone is 24 cm and diameter of the base is 14 cm, then the slant height of the cone is 15 cm.
Reason (R): If r be the radius of the cone and h be the height of the cone, then slant height =
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Vivek Rana answered |
Slant height = 
which proves that assertion is wrong.
Therefore, A is false but R is true.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. The volume of the solid is π cm3.Reason (R): Volume of cone = 
and volume of hemi-sphere = 
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. The volume of the solid is π cm3.
Reason (R): Volume of cone = and volume of hemi-sphere =
and volume of hemi-sphere = a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Kiran Mehta answered |
Volume of the Solid = 
Which is true.
Therefore, Both A and R are true and R is the correct explanation for A.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : No. of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm. in diameter, is 2541Reason : Number of balls 
- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'C'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : No. of spherical balls that can be made out of a solid cube of lead whose edge is 44 cm, each ball being 4 cm. in diameter, is 2541
Reason : Number of balls
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Rohit Sharma answered |
N * (volume of small spheres) = total volume
n ∗ (4/3) ∗ (22/7) ∗ 23 = (44)3
n = (3/4) ∗ (7/22) ∗ (1/8) ∗ (44)3 = 2541
As per the given reason, n = (volume of one ball)/(volume of lead)
Thus, reason is not correct but assertion is correct.
The shape of a glass (tumbler) (see Fig.) is usually in the form of
- a)a cone
- b)frustum of a cone
- c)a cylinder
- d)a sphere
Correct answer is option 'B'. Can you explain this answer?
The shape of a glass (tumbler) (see Fig.) is usually in the form of
a)
a cone
b)
frustum of a cone
c)
a cylinder
d)
a sphere
|
Saxena Aastha answered |
Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum.
so correct option is B
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If the volume of two spheres are in the ratio 27 : 8. Then their surface area are in the ratio 3 : 2.Reason (R): Volume of sphere = 
and its surface area = 4πr2.- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'D'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If the volume of two spheres are in the ratio 27 : 8. Then their surface area are in the ratio 3 : 2.
Reason (R): Volume of sphere = and its surface area = 4πr2.
and its surface area = 4πr2.a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Anita Menon answered |
⇒ 
⇒ 
Let S1 and S2 be the surface area of two spheres,
which proves that assertion is wrong.
Therefore, A is false but R is true.
Let V1, V2 are the volumes of the two spheres.
R and r be the radii of the two spheres.
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): A manufacturer involved children in colouring playing top (Lattu) which is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. The area to be painted if 100 playing tops are given to him then will be 3955 cm2.Reason (R): Slant height = 
- a)Both A and R are true and R is the correct explanation of A.
- b)Both A and R are true and R is not correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'C'. Can you explain this answer?
Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): A manufacturer involved children in colouring playing top (Lattu) which is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. The area to be painted if 100 playing tops are given to him then will be 3955 cm2.
Reason (R): Slant height =
a)
Both A and R are true and R is the correct explanation of A.
b)
Both A and R are true and R is not correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
|
|
Anita Menon answered |
The formula of slant height is wrong.
The correct formula is l = 
Therefore, A is true but R is false.
Chapter doubts & questions for Mensuration - Mathematics for SSS 1 2024 is part of SSS 1 exam preparation. The chapters have been prepared according to the SSS 1 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for SSS 1 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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