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All questions of Surface Area & Volumes for Class 9 Exam
A rectangular sand box is 5 m wide and 2 m long. How many cubic metres of sand are needed to fill the box upto a depth of 10 cm ?- a)1
- b)10
- c)100
- d)1000
Correct answer is option 'A'. Can you explain this answer?
A rectangular sand box is 5 m wide and 2 m long. How many cubic metres of sand are needed to fill the box upto a depth of 10 cm ?
a)
1
b)
10
c)
100
d)
1000
 | Arizona Academy answered |
To calculate the volume of sand needed to fill the rectangular sandbox, we can use the formula:Volume = Length × Width × DepthGiven:
Length = 2 m
Width = 5 m
Depth = 10 cm = 0.1 mSubstituting the values into the formula:Volume = 2 m × 5 m × 0.1 m
Volume = 1 cubic meterTherefore, the correct answer is A: 1 cubic meter.
Length = 2 m
Width = 5 m
Depth = 10 cm = 0.1 mSubstituting the values into the formula:Volume = 2 m × 5 m × 0.1 m
Volume = 1 cubic meterTherefore, the correct answer is A: 1 cubic meter.
A conical tomb of base diameter 24m and height 16 m. What is the curved surface area?- a)200π sq m
- b)240π sq m
- c)300π sq m
- d)64π sq m
Correct answer is option 'B'. Can you explain this answer?
A conical tomb of base diameter 24m and height 16 m. What is the curved surface area?
a)
200π sq m
b)
240π sq m
c)
300π sq m
d)
64π sq m
 | Sagnik Menon answered |
The formula for the curved surface area of a cone is πrs, where r is the radius of the base and s is the slant height. To find the slant height, we can use the Pythagorean theorem: s² = r² + h², where h is the height of the cone.
In this case, the radius is half of the base diameter, so r = 12m. Using the Pythagorean theorem, we get:
s² = 12² + 16²
s² = 144 + 256
s² = 400
s = 20m
Now we can calculate the curved surface area:
A = πrs
A = π(12)(20)
A = 240π
Using a calculator, we can approximate this to:
A ≈ 753.98
Therefore, the curved surface area of the conical tomb is approximately 753.98 square meters.
In this case, the radius is half of the base diameter, so r = 12m. Using the Pythagorean theorem, we get:
s² = 12² + 16²
s² = 144 + 256
s² = 400
s = 20m
Now we can calculate the curved surface area:
A = πrs
A = π(12)(20)
A = 240π
Using a calculator, we can approximate this to:
A ≈ 753.98
Therefore, the curved surface area of the conical tomb is approximately 753.98 square meters.
A beam 9 m long, 40 cm wide and 20 cm deep is made up of iron which weighs 50 kg per cubic metre.The weight of the beam is :- a)27 kg
- b)36 kg
- c)48 kg
- d)56 kg
Correct answer is option 'B'. Can you explain this answer?
A beam 9 m long, 40 cm wide and 20 cm deep is made up of iron which weighs 50 kg per cubic metre.
The weight of the beam is :
a)
27 kg
b)
36 kg
c)
48 kg
d)
56 kg
| | Arizona Academy answered |
To find the weight of the iron beam, we need to calculate its volume and then multiply it by the weight of 1 cubic meter of iron, which is given as 50 kg.Given:
Length of beam (l) = 9 m
Breadth (b) = 40 cm = 0.4 m
Height (h) = 20 cm = 0.2 m
Weight of 1 cubic meter of iron = 50 kgVolume of the beam = l × b × h = 9 m × 0.4 m × 0.2 m = 0.72 cubic metersWeight of the beam = Volume × Weight of 1 cubic meter of iron = 0.72 cubic meters × 50 kg/cubic meter = 36 kg
Length of beam (l) = 9 m
Breadth (b) = 40 cm = 0.4 m
Height (h) = 20 cm = 0.2 m
Weight of 1 cubic meter of iron = 50 kgVolume of the beam = l × b × h = 9 m × 0.4 m × 0.2 m = 0.72 cubic metersWeight of the beam = Volume × Weight of 1 cubic meter of iron = 0.72 cubic meters × 50 kg/cubic meter = 36 kg
Therefore, the weight of the iron beam is 36 kg, which corresponds to option B.
The curved surface area of a right circular cone whose slant height is 14 cm and base radius is 21 cm is- a)308 cm2
- b)924 cm2
- c)232 cm2
- d)446 cm2
Correct answer is option 'B'. Can you explain this answer?
The curved surface area of a right circular cone whose slant height is 14 cm and base radius is 21 cm is
a)
308 cm2
b)
924 cm2
c)
232 cm2
d)
446 cm2
 | Krish Grover answered |
( b ) 924
L = 14 cm
R = 21 cm
C S A of Cone = πRL
22 / 7 * 21 * 14 cm
22 * 21 * 2 cm
462 * 2 cm
924 centimetre square
L = 14 cm
R = 21 cm
C S A of Cone = πRL
22 / 7 * 21 * 14 cm
22 * 21 * 2 cm
462 * 2 cm
924 centimetre square
The surface area of a cube of side 27 cm is :- a)2916 cm2
- b)729 cm2
- c)4374 cm2
- d)19683 cm2
Correct answer is option 'C'. Can you explain this answer?
The surface area of a cube of side 27 cm is :
a)
2916 cm2
b)
729 cm2
c)
4374 cm2
d)
19683 cm2
| | Arizona Academy answered |
The surface area of a cube of side 27 cm can be found using the formula:Surface area of a cube = 6a^2, where a is the length of the side of the cube.Given:
Length of side of the cube = 27 cmSubstituting the value into the formula:Surface area of the cube = 6 × 27^2
Surface area of the cube = 6 × 729
Surface area of the cube = 4374 cm^2Therefore, the surface area of the cube of side 27 cm is 4374 cm^2, which corresponds to option C
Length of side of the cube = 27 cmSubstituting the value into the formula:Surface area of the cube = 6 × 27^2
Surface area of the cube = 6 × 729
Surface area of the cube = 4374 cm^2Therefore, the surface area of the cube of side 27 cm is 4374 cm^2, which corresponds to option C
The total surface area of a cube is 96 cm2 . The volume of the cube is- a)64 cm3
- b)27 cm3
- c)512 cm3
- d)9 cm3
Correct answer is option 'A'. Can you explain this answer?
The total surface area of a cube is 96 cm2 . The volume of the cube is
a)
64 cm3
b)
27 cm3
c)
512 cm3
d)
9 cm3
 | Aamna Adil answered |
Tsa of cube=6a²
volume of cube=a³
6a²=96
a²=96/6
a²=16
a=4
volume =a³
4³=4×4×4
64cm³
volume of cube=a³
6a²=96
a²=96/6
a²=16
a=4
volume =a³
4³=4×4×4
64cm³
If the outer diameter of a pipe 21 m long is 1 m, then its curved surface area is- a)66 m2
- b)21 m2
- c)42 m2
- d)63 m2
Correct answer is option 'A'. Can you explain this answer?
If the outer diameter of a pipe 21 m long is 1 m, then its curved surface area is
a)
66 m2
b)
21 m2
c)
42 m2
d)
63 m2
| | Prateek Kushwaha answered |
Use formula of corved surface area..
2¶rh
2¶rh
The radius of two similar right circular cones are 2 cm and 6 cm. The ratio of their volumes is- a)1 : 3
- b)1 : 9
- c)9 : 1
- d)1 : 27
Correct answer is option 'D'. Can you explain this answer?
The radius of two similar right circular cones are 2 cm and 6 cm. The ratio of their volumes is
a)
1 : 3
b)
1 : 9
c)
9 : 1
d)
1 : 27
 | Nilanjan Sharma answered |
Let the volume two cones be v1 & v2 & r1 and r2 be the radii of the two right circular cones & height of the two cones be h.
Ratio of base radii = r1:r2= 3 : 5
Volume of cone = 1/3πr^2h
Volume of first cone (v1)1/Volume of second cone (v2)
=(1/3�π�r1^2�h)/(1/3�π�r2^2�h)
= (1/3�π�3^2�h)/(1/3�π�5^2�h)
= r1^2/r2^2
= 3^2/5^2
= 9/25
= 9 : 25
Hence, the ratio of their volumes is 9 : 25
The area surrounded by a conical tent is 4526 m2. If the cost of canvas is Rs. 17 per square meter, then find the total cost of canvas.- a)Rs. 52100
- b)Rs. 76942
- c)Rs. 65000
- d)Rs. 85246
Correct answer is option 'B'. Can you explain this answer?
The area surrounded by a conical tent is 4526 m2. If the cost of canvas is Rs. 17 per square meter, then find the total cost of canvas.
a)
Rs. 52100
b)
Rs. 76942
c)
Rs. 65000
d)
Rs. 85246
| | Arun Sharma answered |
total cost = area of canvas used x cost of per meter square canvas
= 4526 x 17
= Rs. 76942
The cost of cementing the inner curved surface of a 14 m deep well of radius 2 m at the rate of Rs 2 per m2 is- a)Rs 352.
- b)Rs 176.
- c)Rs 56.
- d)Rs 112.
Correct answer is option 'A'. Can you explain this answer?
The cost of cementing the inner curved surface of a 14 m deep well of radius 2 m at the rate of Rs 2 per m2 is
a)
Rs 352.
b)
Rs 176.
c)
Rs 56.
d)
Rs 112.
 | Kamna Science Academy answered |
Depth of well(h) = 14m
radius of well(r) = 2m
radius of well(r) = 2m
Inner surface area of well(like a cylinder) = 2πrh
surface area= 2 x 22/7 x 2 x 14 = 176 m2
cost of cementing = ₹2 per m2
Total Cost = 176 x 2 = ₹352
The volume of a spherical shell whose internal and external diameters are 8 cm and 10 cm respectively (in cubic cm) is:- a)122π/3
- b)244π/3
- c)212
- d)257
Correct answer is option 'B'. Can you explain this answer?
The volume of a spherical shell whose internal and external diameters are 8 cm and 10 cm respectively (in cubic cm) is:
a)
122π/3
b)
244π/3
c)
212
d)
257
 | Sarita Reddy answered |
The volume of a spherical shell is the difference between the volumes of the two spheres that make up the shell. The internal sphere has a diameter of 8 cm, and the external sphere has a diameter of 10 cm. To find the volume of the spherical shell, we can first find the volume of each of the two spheres and then subtract the volume of the smaller sphere from the volume of the larger sphere.
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume, r is the radius of the sphere, and π is a mathematical constant approximately equal to 3.14159. The radius of the internal sphere is 4 cm (half of the diameter), and the radius of the external sphere is 5 cm (half of the diameter). Therefore, the volume of the internal sphere is (4/3)π(4^3) = (4/3)π64 = 256π/3 cubic cm, and the volume of the external sphere is (4/3)π(5^3) = (4/3)π125 = 500π/3 cubic cm.
To find the volume of the spherical shell, we subtract the volume of the internal sphere from the volume of the external sphere: 500π/3 - 256π/3 = 244π/3 cubic cm. Therefore, the volume of the spherical shell is 244π/3 cubic cm, which corresponds to answer choice (b).
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is :- a)1 : 2
- b)1 : 4
- c)1 : 8
- d)1 : 16
Correct answer is option 'B'. Can you explain this answer?
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is :
a)
1 : 2
b)
1 : 4
c)
1 : 8
d)
1 : 16
| | Sarita Reddy answered |
The correct answer is option 'B', the ratio of surface areas is 1:4.
The ratio of the surface areas of two spheres is the square of the ratio of their radii. If the ratio of volumes of two spheres is 1:8, then the ratio of their radii is 3:2 . Therefore, the ratio of the surface areas of the two spheres is (3/2)^2 = 9/4 = 1:4
If the curved surface area of a cylinder is 1760 sq. cm and its base radius is 14 cm, then its height is :- a)10 cm
- b)15 cm
- c)20 cm
- d)40 cm
Correct answer is option 'C'. Can you explain this answer?
If the curved surface area of a cylinder is 1760 sq. cm and its base radius is 14 cm, then its height is :
a)
10 cm
b)
15 cm
c)
20 cm
d)
40 cm
| | Sarthak Satav answered |
I think answer is 40 cm because
C.S.A. OF CYLINDER = 2πrh
1760 cm² = 2 x 22/7 x 14 x h
(1760 x 7 ) / 22 x 2 x 14 = h
that is
40 cm
C.S.A. OF CYLINDER = 2πrh
1760 cm² = 2 x 22/7 x 14 x h
(1760 x 7 ) / 22 x 2 x 14 = h
that is
40 cm
The total surface area of a hemispherical bowl of diameter 28 cm is- a)1848 cm2
- b)1800 cm2
- c)1600 cm2
- d)1648 cm2
Correct answer is option 'A'. Can you explain this answer?
The total surface area of a hemispherical bowl of diameter 28 cm is
a)
1848 cm2
b)
1800 cm2
c)
1600 cm2
d)
1648 cm2
| | Sarita Reddy answered |
Correct, option 'A' is the correct answer.
The total surface area of a hemispherical bowl can be calculated by using the formula 4πr^2, where r is the radius of the bowl.
Given the diameter of the bowl is 28 cm, the radius of the bowl is 14cm.
So, the total surface area of the hemispherical bowl of diameter 28 cm is 4π(14)^2 = 4π*196 =784π = 1848 cm^2 (approximately)
Alternatively, we can also use the formula 2πr^2 + 2πrr (r being the radius of the bowl) to calculate the total surface area of the hemispherical bowl.
In this case, 2π(14)^2 + 2π(14) 14 = 2π196 + 2π196 = 392π = 1848 cm^2 (approximately)
Hence the answer is A. 1848 cm2
If a hemi-spherical dome has an inner diameter of 28 m, then its volume (in m3) is :- a)6186.60
- b)5749.33
- c)7099.33
- d)7459.33
Correct answer is option 'B'. Can you explain this answer?
If a hemi-spherical dome has an inner diameter of 28 m, then its volume (in m3) is :
a)
6186.60
b)
5749.33
c)
7099.33
d)
7459.33
| | Sarita Reddy answered |
Correct, option 'B' is the correct answer.
The volume of a hemisphere can be calculated using the formula, V = 2/3 * π * r^3, where r is the radius of the hemisphere.
A hemi-spherical dome has an inner diameter of 28 m, so the radius of the hemisphere is half of the diameter which is 14m.
So, the volume of the hemi-spherical dome is: 2/3 * π * (14)^3 = 2/3 * π * 2744 = 5749.33 m^3 (approximately)
Hence the answer is B. 5749.33 m^3
If the radius of a sphere is reduced by a factor of 3. Its volume is- a)reduced by 1/9 of the former volume.
- b)increased by 1/9 of the former volume
- c)reduced by 1/27 of the former volume.
- d)increased by 1/27 of the former volume
Correct answer is option 'C'. Can you explain this answer?
If the radius of a sphere is reduced by a factor of 3. Its volume is
a)
reduced by 1/9 of the former volume.
b)
increased by 1/9 of the former volume
c)
reduced by 1/27 of the former volume.
d)
increased by 1/27 of the former volume
| | Ankita answered |
Reduced by 1/27 of the former volume, Option C.
The solid generated by the rotation of a right triangle about one of its sides containing the right angle is called a ………- a)Hemisphere
- b)Right circular cylinder
- c)Right circular cone
- d)Cube
Correct answer is option 'C'. Can you explain this answer?
The solid generated by the rotation of a right triangle about one of its sides containing the right angle is called a ………
a)
Hemisphere
b)
Right circular cylinder
c)
Right circular cone
d)
Cube
 | Raj Kumar answered |
When the triangle is rotated about its side it becomes the height of the cone and the other side containing the right angle becomes the radius..
The diameter of a sphere whose volume is 1047.816 cm3 is- a)8.6 cm
- b)10.6 cm
- c)16.6 cm
- d)12.6 cm
Correct answer is option 'D'. Can you explain this answer?
The diameter of a sphere whose volume is 1047.816 cm3 is
a)
8.6 cm
b)
10.6 cm
c)
16.6 cm
d)
12.6 cm
 | Abhay Chawla answered |
Given: Volume of the sphere = 1047.816 cm³
To find: Diameter of the sphere
Formula used: Volume of sphere = (4/3)πr³, where r is the radius of the sphere
Explanation:
We know that the volume of the sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.
We can find the radius of the sphere by using the formula:
r = (3V/4π)^(1/3), where V is the volume of the sphere.
Substituting the given value of V, we get:
r = (3 x 1047.816/4π)^(1/3)
r = 6.3 cm (approx.)
Now, we can find the diameter of the sphere by multiplying the radius by 2.
Diameter = 2 x radius
Diameter = 2 x 6.3
Diameter = 12.6 cm
Therefore, the diameter of the sphere is 12.6 cm, which is option D.
To find: Diameter of the sphere
Formula used: Volume of sphere = (4/3)πr³, where r is the radius of the sphere
Explanation:
We know that the volume of the sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.
We can find the radius of the sphere by using the formula:
r = (3V/4π)^(1/3), where V is the volume of the sphere.
Substituting the given value of V, we get:
r = (3 x 1047.816/4π)^(1/3)
r = 6.3 cm (approx.)
Now, we can find the diameter of the sphere by multiplying the radius by 2.
Diameter = 2 x radius
Diameter = 2 x 6.3
Diameter = 12.6 cm
Therefore, the diameter of the sphere is 12.6 cm, which is option D.
Given that 1 cm3 of a metal weighs 5 gms, the weight of a cylindrical metal container with base radius 10.5 cm and height 60 cm, is :- a)97.65 kg
- b)48.75 kg
- c)103.95 kg
- d)102.45 kg
Correct answer is option 'C'. Can you explain this answer?
Given that 1 cm3 of a metal weighs 5 gms, the weight of a cylindrical metal container with base radius 10.5 cm and height 60 cm, is :
a)
97.65 kg
b)
48.75 kg
c)
103.95 kg
d)
102.45 kg
| | Arizona Academy answered |
Given:
Radius = 10.5 cm
Height = 6 m
Weight of 1 cm3 = 5 grams
Formula used:
Volume of cylinder = πr2h
1 m = 100 cm
⇒ 6 m = 600 cm
1 kg = 1000 gram
Calculation:
According to the question
Volume of cylinder = πr2h
⇒ (3.14 × 10.5 × 10.5 × 600) cm3
⇒ 207711 cm3
Now, Weight of 1 cm3 = 5 grams
So, Weight of 207,711 cm3 = 5 × 207711
⇒ 1,038,555 grams
⇒ 1038.555 kg ~ 1038.5 kg
The surface area of a sphere of radius 7 cm is- a)636 cm2
- b)616 cm2
- c)702 cm2
- d)546 cm2
Correct answer is option 'B'. Can you explain this answer?
The surface area of a sphere of radius 7 cm is
a)
636 cm2
b)
616 cm2
c)
702 cm2
d)
546 cm2
| | Kumar Aryan answered |
As we know that the formula of surface area of a sphere is 4πr
here the given radius is 7cm
so by using formula of surface area of sphere we find that
=> 4×7×7×22÷7 = 616 cm²
which is option (b).
here the given radius is 7cm
so by using formula of surface area of sphere we find that
=> 4×7×7×22÷7 = 616 cm²
which is option (b).
A conical tent is 15 m high and the radius of its base is 20 m. The cost of the canvas required to make the tent at the rate of Rs 7 per m2 is- a)Rs 10000
- b)Rs 12000
- c)Rs 11000
- d)Rs 9000
Correct answer is option 'C'. Can you explain this answer?
A conical tent is 15 m high and the radius of its base is 20 m. The cost of the canvas required to make the tent at the rate of Rs 7 per m2 is
a)
Rs 10000
b)
Rs 12000
c)
Rs 11000
d)
Rs 9000
 | Aditi Bhosale answered |
Given-Height-h-15m, radius-r-20m
So, l=√(r)²+(h)²
=√(20)²+(15)²=√400+225=√625=25m
Now, CSA of conical tent=πrl
=22/7×20×25
=11000/7cm²
Total cost of canvas required to mke tent=Area of conical tent×rate per m²
=11000/7×7
=₹11000, so option 'C' is correct
So, l=√(r)²+(h)²
=√(20)²+(15)²=√400+225=√625=25m
Now, CSA of conical tent=πrl
=22/7×20×25
=11000/7cm²
Total cost of canvas required to mke tent=Area of conical tent×rate per m²
=11000/7×7
=₹11000, so option 'C' is correct
The volume of a cube with surface area 384 sq. cm, is :- a)216 cm3
- b)256 cm3
- c)484 cm3
- d)512 cm3
Correct answer is option 'D'. Can you explain this answer?
The volume of a cube with surface area 384 sq. cm, is :
a)
216 cm3
b)
256 cm3
c)
484 cm3
d)
512 cm3
 | Sanjana Bose answered |
The surface area of a cube is given by 6 times the area of one face, and the area of a face of a cube is equal to the length of one edge squared. So if the surface area of the cube is 384 cm^2, we can write the equation:
6 * edge^2 = 384
Solving for the edge length:
edge^2 = 64
edge = 8
The volume of a cube is equal to the length of one edge cubed, so the volume of this cube is:
volume = 8^3 = 512 cm^3
A sphere has a surface area of 301.84 cm2. Its diameter is- a)8.4 cm
- b)7.4 cm
- c)9.8 cm
- d)10.6 cm
Correct answer is option 'C'. Can you explain this answer?
A sphere has a surface area of 301.84 cm2. Its diameter is
a)
8.4 cm
b)
7.4 cm
c)
9.8 cm
d)
10.6 cm
 | Bishwanath Patra answered |
Surface area of sphere= 301.84 cm^2, 4 × 22/7 ×r^2 =301.84 , r^2 = 301.84 ×7 / 22, r^2 = 24.01 r = 4.9cm , diameter = 2r =2×4.9 =9.8cm
The length of the longest rod that can fit in a cubical vessel of side 10 cm, is- a)10 cm
- b)10√2 cm
- c)10√3 cm
- d)20 cm
Correct answer is option 'C'. Can you explain this answer?
The length of the longest rod that can fit in a cubical vessel of side 10 cm, is
a)
10 cm
b)
10√2 cm
c)
10√3 cm
d)
20 cm
| | Bably Bhatt answered |
The longest stick that can be fit is the length of the diagonal of the cubical vessel.
Therefore, length of diagonal =(10)2+(10)2+(10)2 =3(10)2=103cm
Therefore, length of diagonal =(10)2+(10)2+(10)2 =3(10)2=103cm
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