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All questions of Mensuration: Volume, Surface Area & Solid Figures for RRB NTPC/ASM/CA/TA Exam
Find the perimeter of the a square with side 4cm.- a)16 cm
- b)12 cm
- c)10 cm
- d)8 cm
Correct answer is option 'A'. Can you explain this answer?
Find the perimeter of the a square with side 4cm.
a)
16 cm
b)
12 cm
c)
10 cm
d)
8 cm
|
Sreesha Phalod answered |
Sol. perimeter of square=4* sides
=4*4 (sides is 4)
=16.
=4*4 (sides is 4)
=16.
ABCD is a square of side 10 cm. What is the area of the least-sized square that may be inscribed in ABCD with its vertices on the sides of ABCD?- a)0 cm2
- b)25 cm2
- c)50 cm2
- d)66.66 cm2
Correct answer is option 'A'. Can you explain this answer?
ABCD is a square of side 10 cm. What is the area of the least-sized square that may be inscribed in ABCD with its vertices on the sides of ABCD?
a)
0 cm2
b)
25 cm2
c)
50 cm2
d)
66.66 cm2
|
Athira Sen answered |
The vertices of the smaller square will be on the midpoints of the sides of the larger square.
Find the volume of a cuboid whose length is 8 cm, width is 3 cm and height is 5 cm. - a)135 cm3
- b)125 cm3
- c)120 cm3
- d)130 cm3
Correct answer is option 'C'. Can you explain this answer?
Find the volume of a cuboid whose length is 8 cm, width is 3 cm and height is 5 cm.
a)
135 cm3
b)
125 cm3
c)
120 cm3
d)
130 cm3
|
Tanishq Joshi answered |
Finding Volume of a Cuboid
Given: length = 8 cm, width = 3 cm, height = 5 cm
To find: Volume of the cuboid
Formula: Volume of a cuboid = length x width x height
Substituting the given values in the formula, we get:
Volume = 8 cm x 3 cm x 5 cm
Volume = 120 cm3
Therefore, the correct answer is option C, 120 cm3.
Given: length = 8 cm, width = 3 cm, height = 5 cm
To find: Volume of the cuboid
Formula: Volume of a cuboid = length x width x height
Substituting the given values in the formula, we get:
Volume = 8 cm x 3 cm x 5 cm
Volume = 120 cm3
Therefore, the correct answer is option C, 120 cm3.
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Mensuration, Class 8, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic. Q.Find the volume of a cuboid whose length is 8 cm, breadth 6 cm and height 3.5 cm. - a)215 cm3
- b)172 cm3
- c)150 cm3
- d)168 cm3
Correct answer is option 'D'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter Mensuration, Class 8, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.
Q.
Find the volume of a cuboid whose length is 8 cm, breadth 6 cm and height 3.5 cm.
a)
215 cm3
b)
172 cm3
c)
150 cm3
d)
168 cm3
|
Ankita Shah answered |
Given,
Length (l) = 8 cm
Breadth (b) = 6 cm
Height (h) = 3.5 cm
We know that the volume of a cuboid is given by the formula:
Volume = length × breadth × height
Substituting the given values, we get:
Volume = 8 cm × 6 cm × 3.5 cm
Volume = 168 cm³
Therefore, the volume of the given cuboid is 168 cm³.
Hence, the correct option is (d) 168 cm³.
Length (l) = 8 cm
Breadth (b) = 6 cm
Height (h) = 3.5 cm
We know that the volume of a cuboid is given by the formula:
Volume = length × breadth × height
Substituting the given values, we get:
Volume = 8 cm × 6 cm × 3.5 cm
Volume = 168 cm³
Therefore, the volume of the given cuboid is 168 cm³.
Hence, the correct option is (d) 168 cm³.
Find the area of a triangle whose base is 4 cm and altitude is 6 cm.- a)10 cm2
- b)14 cm2
- c)16 cm2
- d)12 cm2
Correct answer is option 'D'. Can you explain this answer?
Find the area of a triangle whose base is 4 cm and altitude is 6 cm.
a)
10 cm2
b)
14 cm2
c)
16 cm2
d)
12 cm2
|
Kavya Saxena answered |
We know that area of triangle is equals to 1/2 base × altitude.
Here, base = 4 cm and altitude = 6 cm.
So, area = 1/2 × 4 × 6= 24 /2= 12 cm2.
Here, base = 4 cm and altitude = 6 cm.
So, area = 1/2 × 4 × 6= 24 /2= 12 cm2.
What is the area of an equilateral triangle of side 16 cm?- a)48√3 cm2
- b)128√3 cm2
- c)9.6√3 cm2
- d)64√3 cm2
Correct answer is option 'D'. Can you explain this answer?
What is the area of an equilateral triangle of side 16 cm?
a)
48√3 cm2
b)
128√3 cm2
c)
9.6√3 cm2
d)
64√3 cm2
|
|
Vt Sir - Kota answered |
Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2
PQRST is a pentagon in which all the interior angles are unequal. A circle of radius ‘r’ is inscribed in each of the vertices. Find the area of portion of circles falling inside the pentagon. - a)πr2
- b)1.5πr2
- c)2πr2
- d)1.25πr2
Correct answer is option 'B'. Can you explain this answer?
PQRST is a pentagon in which all the interior angles are unequal. A circle of radius ‘r’ is inscribed in each of the vertices. Find the area of portion of circles falling inside the pentagon.
a)
πr2
b)
1.5πr2
c)
2πr2
d)
1.25πr2
|
Preeti Khanna answered |
Since neither angles nor sides are given in the question, immediately the sum of angles of pentagon should come in mind. To use it,
We know the area of the sectors of a circle is given as,
We know the area of the sectors of a circle is given as,
Note => The above concept is applicable for a polygon of n sides.
Choice (B) is therefore, the correct answer.
Correct Answer: 1.5πr2
Choice (B) is therefore, the correct answer.
Correct Answer: 1.5πr2
There is a right circular cone with base radius 3 units and height 4 units. The surface of this right circular cone is painted. It is then cut into two parts by a plane parallel to the base so that the volume of the top part (the small cone) divided by the volume of the frustum equals the painted area of the top part divided by the painted area of the bottom part. The height of the small cone is- a)7/3
- b)5/4
- c)5/2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
There is a right circular cone with base radius 3 units and height 4 units. The surface of this right circular cone is painted. It is then cut into two parts by a plane parallel to the base so that the volume of the top part (the small cone) divided by the volume of the frustum equals the painted area of the top part divided by the painted area of the bottom part. The height of the small cone is
a)
7/3
b)
5/4
c)
5/2
d)
None of these
|
|
Kajal Kumar answered |
Take the total surface area of the initial cone into consideration and then proceed.
Four spheres each of radius 10 cm lie on a horizontal table so that the centres of the spheres form a square of side 20 cm. A fifth sphere also of radius 10 cm is placed on them so that it touches each of these spheres without disturbing them. How many cm above the table is the centre of the fifth sphere?- a)10√6
- b)10(1 + √2)
- c)10(1 + √3)
- d)10(4 - √2)
Correct answer is option 'B'. Can you explain this answer?
Four spheres each of radius 10 cm lie on a horizontal table so that the centres of the spheres form a square of side 20 cm. A fifth sphere also of radius 10 cm is placed on them so that it touches each of these spheres without disturbing them. How many cm above the table is the centre of the fifth sphere?
a)
10√6
b)
10(1 + √2)
c)
10(1 + √3)
d)
10(4 - √2)
|
Hridoy Mehra answered |
OA= 10
OA= 10
To find the value of PA, go through the options now.
To find the value of PA, go through the options now.
PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters. Areas A and B are marked. A/B is equal to:
- a)π
- b)1
- c)π/4
- d)2
Correct answer is option 'B'. Can you explain this answer?
PQRS is a circle and circles are drawn with PO, QO, RO and SO as diameters. Areas A and B are marked. A/B is equal to:
a)
π
b)
1
c)
π/4
d)
2
|
Divey Sethi answered |
Such questions are all about visualization and ability to write one area in terms of others.
Here, Let the radius of PQRS be 2r
∴ Radius of each of the smaller circles = 2r/2 = r
∴ Area A can be written as:
A = π (2r)2 – 4 x π(r)2 (Area of the four smaller circles) + B (since, B has been counted twice in the previous subtraction)
Here, Let the radius of PQRS be 2r
∴ Radius of each of the smaller circles = 2r/2 = r
∴ Area A can be written as:
A = π (2r)2 – 4 x π(r)2 (Area of the four smaller circles) + B (since, B has been counted twice in the previous subtraction)
A = 4πr2 - 4πr2 + B
A = B
A/B = 1
A = B
A/B = 1
Choice (B) is therefore, the correct answer.
Correct Answer: 1
Correct Answer: 1
If the edge of a cube is 1 cm then which of the following is its total surface area?- a)1 cm2
- b)4 cm2
- c)6 cm2
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If the edge of a cube is 1 cm then which of the following is its total surface area?
a)
1 cm2
b)
4 cm2
c)
6 cm2
d)
none of these
|
|
Stuti Basak answered |
Explanation:
To find the total surface area of a cube, we need to find the area of all its six faces and add them up. Since all the faces of a cube are identical squares, we can find the area of one face and multiply it by 6 to get the total surface area.
Given, the edge of the cube is 1 cm. Therefore, the area of one face of the cube is:
Area of square = side × side
Area of square = 1 cm × 1 cm
Area of square = 1 cm²
To find the total surface area of the cube, we need to multiply the area of one face by 6:
Total surface area of cube = 6 × area of one face
Total surface area of cube = 6 × 1 cm²
Total surface area of cube = 6 cm²
Therefore, the total surface area of the cube is 6 cm², which is option C.
To find the total surface area of a cube, we need to find the area of all its six faces and add them up. Since all the faces of a cube are identical squares, we can find the area of one face and multiply it by 6 to get the total surface area.
Given, the edge of the cube is 1 cm. Therefore, the area of one face of the cube is:
Area of square = side × side
Area of square = 1 cm × 1 cm
Area of square = 1 cm²
To find the total surface area of the cube, we need to multiply the area of one face by 6:
Total surface area of cube = 6 × area of one face
Total surface area of cube = 6 × 1 cm²
Total surface area of cube = 6 cm²
Therefore, the total surface area of the cube is 6 cm², which is option C.
All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is 3 cm. The total area of all its surfaces (in cm2) is- a)8
- b)10
- c)12
- d)16
Correct answer is option 'C'. Can you explain this answer?
All five faces of a regular pyramid with a square base are found to be of the same area. The height of the pyramid is 3 cm. The total area of all its surfaces (in cm2) is
a)
8
b)
10
c)
12
d)
16
|
|
Prateek Menon answered |
Equate the area of the square ABCD and triangle PDC and find a relation between the slant height and the length of the base of the pyramid
The length of each side of a cube is 24 cm. The volume of the cube is equal to the volume of a cuboid. If the breadth and the height of the cuboid are 32 cm and 12 cm, respectively, then what will be the length of the cuboid?- a)36
- b)27
- c)16
- d)20
Correct answer is option 'A'. Can you explain this answer?
The length of each side of a cube is 24 cm. The volume of the cube is equal to the volume of a cuboid. If the breadth and the height of the cuboid are 32 cm and 12 cm, respectively, then what will be the length of the cuboid?
a)
36
b)
27
c)
16
d)
20
|
C K Academy answered |
Given:
The length of each side of a cube is 24 cm.
The breadth and the height of the cuboid are 32 cm and 12 cm, respectively.
The length of each side of a cube is 24 cm.
The breadth and the height of the cuboid are 32 cm and 12 cm, respectively.
Concept used:
The volume of the cube is equal to the volume of a cuboid.
Volume of cube = a³
Volume of cuboid = lbh
The volume of the cube is equal to the volume of a cuboid.
Volume of cube = a³
Volume of cuboid = lbh
Calculation:
The volume of the cube is equal to the volume of a cuboid.
⇒ 24³ = l × 32 × 12
⇒ l = 3 × 12
⇒ l = 36
The volume of the cube is equal to the volume of a cuboid.
⇒ 24³ = l × 32 × 12
⇒ l = 3 × 12
⇒ l = 36
∴ Option 1 is the correct answer.
The area of a rectangular field is 52000 m². This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is : - a)210 m
- b)150 m
- c)160 m
- d)123 m
Correct answer is option 'C'. Can you explain this answer?
The area of a rectangular field is 52000 m². This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is :
a)
210 m
b)
150 m
c)
160 m
d)
123 m
|
|
Kavya Saxena answered |
The area of a rhombus is 200 cm², and one of its diagonals is 20 cm. The length of the other diagonal is _____- a)20 cm
- b)20 m
- c)22 cm
- d)22 m
Correct answer is option 'A'. Can you explain this answer?
The area of a rhombus is 200 cm², and one of its diagonals is 20 cm. The length of the other diagonal is _____
a)
20 cm
b)
20 m
c)
22 cm
d)
22 m
|
|
Roshni Chauhan answered |
Understanding the Area of a Rhombus
The area of a rhombus can be calculated using the formula:
- Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
Given Information
- Area = 200 cm²
- One diagonal (d1) = 20 cm
Finding the Other Diagonal
To find the length of the second diagonal (d2), we can rearrange the area formula:
- 200 = (20 * d2) / 2
Now, let's solve for d2:
- First, multiply both sides by 2:
- 400 = 20 * d2
- Next, divide both sides by 20:
- d2 = 400 / 20
- d2 = 20 cm
Conclusion
The length of the other diagonal (d2) is 20 cm.
Final Answer
The correct answer is option 'A' (20 cm).
This shows that both diagonals of the rhombus can be equal, which is a special case where the rhombus is also a square.
The area of a rhombus can be calculated using the formula:
- Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals.
Given Information
- Area = 200 cm²
- One diagonal (d1) = 20 cm
Finding the Other Diagonal
To find the length of the second diagonal (d2), we can rearrange the area formula:
- 200 = (20 * d2) / 2
Now, let's solve for d2:
- First, multiply both sides by 2:
- 400 = 20 * d2
- Next, divide both sides by 20:
- d2 = 400 / 20
- d2 = 20 cm
Conclusion
The length of the other diagonal (d2) is 20 cm.
Final Answer
The correct answer is option 'A' (20 cm).
This shows that both diagonals of the rhombus can be equal, which is a special case where the rhombus is also a square.
Find the number of spheres of the maximum volume that can be accommodated in the above region.- a)324
- b)323
- c)162
- d)161
Correct answer is option 'D'. Can you explain this answer?
Find the number of spheres of the maximum volume that can be accommodated in the above region.
a)
324
b)
323
c)
162
d)
161
|
Aarav Sharma answered |
To find the maximum number of spheres that can be accommodated in a given region, we need to consider the volume of the region and the volume of each sphere.
Given information:
- The region is not specified, but we know it can accommodate spheres.
- The volume of each sphere is also not specified.
To solve this problem, we can follow these steps:
1. Determine the volume of the region:
- The volume of the region is not given in the question.
- Without the volume of the region, it is not possible to find the maximum number of spheres that can be accommodated.
- We need more information about the region to proceed.
2. Determine the volume of each sphere:
- The volume of each sphere is not given in the question.
- Without the volume of each sphere, it is not possible to find the maximum number of spheres that can be accommodated.
- We need more information about the spheres to proceed.
Since we do not have sufficient information about the region or the spheres, we cannot determine the maximum number of spheres that can be accommodated. Therefore, none of the provided options (a, b, c, d) can be considered as the correct answer.
To solve this problem, we would need additional information such as the volume of the region and/or the volume of each sphere. Without these details, it is not possible to find the maximum number of spheres that can be accommodated.
Given information:
- The region is not specified, but we know it can accommodate spheres.
- The volume of each sphere is also not specified.
To solve this problem, we can follow these steps:
1. Determine the volume of the region:
- The volume of the region is not given in the question.
- Without the volume of the region, it is not possible to find the maximum number of spheres that can be accommodated.
- We need more information about the region to proceed.
2. Determine the volume of each sphere:
- The volume of each sphere is not given in the question.
- Without the volume of each sphere, it is not possible to find the maximum number of spheres that can be accommodated.
- We need more information about the spheres to proceed.
Since we do not have sufficient information about the region or the spheres, we cannot determine the maximum number of spheres that can be accommodated. Therefore, none of the provided options (a, b, c, d) can be considered as the correct answer.
To solve this problem, we would need additional information such as the volume of the region and/or the volume of each sphere. Without these details, it is not possible to find the maximum number of spheres that can be accommodated.
John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.- a)4
- b)5
- c)6
- d)7
Correct answer is option 'B'. Can you explain this answer?
John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.
a)
4
b)
5
c)
6
d)
7
|
|
Ashwin Chawla answered |
Consider the length of the string less than or equal to the inradius of the floor. At the comer of the floor you will find a sixth part of a hemisphere and at the centre it will be a hemisphere.
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?- a)Rs. 4082.40
- b)Rs. 3868.80
- c)Rs. 4216.20
- d)Rs. 3642.40
Correct answer is option 'A'. Can you explain this answer?
An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
a)
Rs. 4082.40
b)
Rs. 3868.80
c)
Rs. 4216.20
d)
Rs. 3642.40
|
|
Aarav Sharma answered |
Given:
- Breadth of the first carpet = 6 m
- Length of the first carpet = 1.44 times the breadth
To find:
- Cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet
Formula:
- Area of a rectangle = Length × Breadth
Calculation:
1. Length of the first carpet:
- Length = 1.44 × Breadth
- Length = 1.44 × 6
- Length = 8.64 m
2. Area of the first carpet:
- Area = Length × Breadth
- Area = 8.64 × 6
- Area = 51.84 sq m
3. Increased length and breadth of the second carpet:
- Length = 1.4 × Length of the first carpet
- Length = 1.4 × 8.64
- Length = 12.096 m
- Breadth = 1.25 × Breadth of the first carpet
- Breadth = 1.25 × 6
- Breadth = 7.5 m
4. Area of the second carpet:
- Area = Length × Breadth
- Area = 12.096 × 7.5
- Area = 90.72 sq m
5. Cost of the carpet:
- Cost per sq m = Rs. 45
- Cost of the first carpet = Area of the first carpet × Cost per sq m
- Cost of the first carpet = 51.84 × 45
- Cost of the first carpet = Rs. 2332.80
- Cost of the second carpet = Area of the second carpet × Cost per sq m
- Cost of the second carpet = 90.72 × 45
- Cost of the second carpet = Rs. 4082.40
Therefore, the cost of the carpet whose length and breadth are 40% more and 25% more respectively than the first carpet is Rs. 4082.40, which is option A.
- Breadth of the first carpet = 6 m
- Length of the first carpet = 1.44 times the breadth
To find:
- Cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet
Formula:
- Area of a rectangle = Length × Breadth
Calculation:
1. Length of the first carpet:
- Length = 1.44 × Breadth
- Length = 1.44 × 6
- Length = 8.64 m
2. Area of the first carpet:
- Area = Length × Breadth
- Area = 8.64 × 6
- Area = 51.84 sq m
3. Increased length and breadth of the second carpet:
- Length = 1.4 × Length of the first carpet
- Length = 1.4 × 8.64
- Length = 12.096 m
- Breadth = 1.25 × Breadth of the first carpet
- Breadth = 1.25 × 6
- Breadth = 7.5 m
4. Area of the second carpet:
- Area = Length × Breadth
- Area = 12.096 × 7.5
- Area = 90.72 sq m
5. Cost of the carpet:
- Cost per sq m = Rs. 45
- Cost of the first carpet = Area of the first carpet × Cost per sq m
- Cost of the first carpet = 51.84 × 45
- Cost of the first carpet = Rs. 2332.80
- Cost of the second carpet = Area of the second carpet × Cost per sq m
- Cost of the second carpet = 90.72 × 45
- Cost of the second carpet = Rs. 4082.40
Therefore, the cost of the carpet whose length and breadth are 40% more and 25% more respectively than the first carpet is Rs. 4082.40, which is option A.
In the setup of the previous two questions, how is h related to n?- a)h = √2n
- b)h=√17n
- c)h = n
- d)h = √l3n
Correct answer is option 'C'. Can you explain this answer?
In the setup of the previous two questions, how is h related to n?
a)
h = √2n
b)
h=√17n
c)
h = n
d)
h = √l3n
|
|
Prateek Menon answered |
Equate the lengths of strings obtained from the above two questions.
Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted is- a)10/3
- b)20/3
- c)10
- d)20
Correct answer is option 'A'. Can you explain this answer?
Under the Indian Posts and Telegraph Act 1885, any package in the form of a right circular cylinder will not be accepted if the sum of its height and the diameter of its base exceeds 10 inches. The height (in inches) of a package of maximum volume that would be accepted is
a)
10/3
b)
20/3
c)
10
d)
20
|
|
Hridoy Mehra answered |
Volume is maximum when radius is equal to height.
ABCD is a square drawn inside a square PTRS of sides 4 cm by joining midpoints of the sides PR, PT, TS, SR. Another square is drawn inside ABCD similarly. This process is repeated infinite number of times. Find the sum of all the squares.
- a)16 cm2
- b)28 cm2
- c)32 cm2
- d)Infinite
Correct answer is option 'C'. Can you explain this answer?
ABCD is a square drawn inside a square PTRS of sides 4 cm by joining midpoints of the sides PR, PT, TS, SR. Another square is drawn inside ABCD similarly. This process is repeated infinite number of times. Find the sum of all the squares.
a)
16 cm2
b)
28 cm2
c)
32 cm2
d)
Infinite
|
|
Rajdeep Verma answered |
If we write the infinite series of area of squares:
= 42 + (2√2)2 + 22 + ……. infinite
Since it is a decreasing series sum of infinite terms can be approximated.
= 16 + 8 + 4 +………infinite
The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?- a)Rs 1,08,050
- b)Rs 8,400
- c)Rs 9,300
- d)Rs 8,540
Correct answer is option 'C'. Can you explain this answer?
The cost of white washing one m2 is Rs 50. What will be the maximum amount saved in painting the room in the most economical way, if the sum of the length, breadth and height is 21 m and all the sides are integers (floor is not to be white washed)?
a)
Rs 1,08,050
b)
Rs 8,400
c)
Rs 9,300
d)
Rs 8,540
|
|
Hridoy Mehra answered |
The amount saved would be maximum only when the difference of maximum area and minimum area to be painted is maximum.
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?- a)25 cm2
- b)42 cm2
- c)35 cm2
- d)70 cm2
Correct answer is option 'C'. Can you explain this answer?
The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
a)
25 cm2
b)
42 cm2
c)
35 cm2
d)
70 cm2
|
Yash Patel answered |
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
The maximum distance between two points of the unit cube is- a)√2 + 1
- b)√2
- c)√3
- d)√2 + √3
Correct answer is option 'C'. Can you explain this answer?
The maximum distance between two points of the unit cube is
a)
√2 + 1
b)
√2
c)
√3
d)
√2 + √3
|
|
Ashwin Chawla answered |
The distance from any vertex at the base of the cube to the vertex that is perpendicular along height to the diametrically opposite vertex is required.
We have to calculate DF.
We have to calculate DF.
A cuboid of length 20 m, breadth 15 m and height 12 m is lying on a table. The cuboid is cut into two equal halves by a plane which is perpendicular to the base and passes through a pair of diagonally opposite points of that surface. Then, a second cut is made by a plane which is parallel to the surface of the table again dividing the cuboid into two equal halves. Now this cuboid is divided into four pieces. Out of these four pieces, one piece is now removed from its place. What is the total surface area of the remaining portion of the cuboid?- a)1290 m2
- b)1380 m2
- c)1440 m2
- d)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
A cuboid of length 20 m, breadth 15 m and height 12 m is lying on a table. The cuboid is cut into two equal halves by a plane which is perpendicular to the base and passes through a pair of diagonally opposite points of that surface. Then, a second cut is made by a plane which is parallel to the surface of the table again dividing the cuboid into two equal halves. Now this cuboid is divided into four pieces. Out of these four pieces, one piece is now removed from its place. What is the total surface area of the remaining portion of the cuboid?
a)
1290 m2
b)
1380 m2
c)
1440 m2
d)
Cannot be determined
|
Srishti Joshi answered |
Since we don’t know that the cut is made parallel to which face, we cannot determine the surface area.
Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?- a)4225
- b)4096
- c)4356
- d)Insufficient Data
Correct answer is option 'C'. Can you explain this answer?
Anil grows tomatoes in his backyard which is in the shape of a square. Each tomato takes 1 cm2 in his backyard. This year, he has been able to grow 131 more tomatoes than last year. The shape of the backyard remained a square. How many tomatoes did Anil produce this year?
a)
4225
b)
4096
c)
4356
d)
Insufficient Data
|
|
Naveen Jain answered |
Let the area of backyard be x2 this year and y2 last year
∴ X2- Y2 = 131
=) (X+Y) (X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=) (X+Y) (X-Y) = 131 x 1
=) X+Y = 131
X-Y = 1
=) 2X = 132 =) X = 66
and Y = 65
∴ Number of tomatoes produced this year = 662 = 4356
Choice (C) is therefore, the correct answer.
Correct Answer: 4356
∴ X2- Y2 = 131
=) (X+Y) (X-Y) = 131
Now, 131 is a prime number (a unique one too. Check out its properties on Google). Also, always identify the prime number given in a question. Might be helpful in cracking the solution.
=) (X+Y) (X-Y) = 131 x 1
=) X+Y = 131
X-Y = 1
=) 2X = 132 =) X = 66
and Y = 65
∴ Number of tomatoes produced this year = 662 = 4356
Choice (C) is therefore, the correct answer.
Correct Answer: 4356
The area of the circle is 2464 cm2 and the ratio of the breadth of the rectangle to radius of the circle is 6:7. If the circumference of the circle is equal to the perimeter of the rectangle, then what is the area of the rectangle.- a)1456 cm2
- b)1536 cm2
- c)1254 cm2
- d)5678 cm2
Correct answer is option 'B'. Can you explain this answer?
The area of the circle is 2464 cm2 and the ratio of the breadth of the rectangle to radius of the circle is 6:7. If the circumference of the circle is equal to the perimeter of the rectangle, then what is the area of the rectangle.
a)
1456 cm2
b)
1536 cm2
c)
1254 cm2
d)
5678 cm2
|
Luminary Institute answered |
Area of the circle=πr2
2464 = 22/7 * r2
Radius of the circle=28 cm
Circumference of the circle=2 * π* r =2 * 22/7 * 28
= 176 cm
Breadth of the rectangle=6/7 * 28=24 cm
Perimeter of the rectangle=2 * (l + b)
176 = 2 * (l + 24)
Length of the rectangle = 64 cm
Area of the rectangle = l * b = 24 * 64 = 1536 cm2
The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)- a)154 cm3
- b)100 cm3
- c)126 cm3
- d)Insufficient data
Correct answer is option 'B'. Can you explain this answer?
The square of side 1 cm are cut from four comers of a sheet of tin (having length = 1 and breadth = b) in order to form an open box. If the whole sheet of tin was rolled along its length to form a cylinder, then the volume of the cylinder is equal to (343/4) cm3. Find the volume of the box. (1 and b are integers)
a)
154 cm3
b)
100 cm3
c)
126 cm3
d)
Insufficient data
|
Mrinalini Basu answered |
The length of the rectangle will be equal to the circumference of the base of the cylinder.
If the parallel sides of a parallelogram are 2 cm apart and their sum is 10 cm then its area is:- a)20 cm2
- b)5 cm2
- c)10 cm2
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If the parallel sides of a parallelogram are 2 cm apart and their sum is 10 cm then its area is:
a)
20 cm2
b)
5 cm2
c)
10 cm2
d)
none of these
|
|
Srestha Menon answered |
Understanding the Parallelogram Area
To find the area of a parallelogram, we can use the formula:
Area = base × height
Where:
- The base is the length of one of the parallel sides.
- The height is the perpendicular distance between the parallel sides.
Given Information
- The distance between the parallel sides (height) = 2 cm
- The sum of the lengths of the parallel sides = 10 cm
Finding the Base
Since we have the sum of the two parallel sides, we can define their lengths as follows:
Let one side be "a" and the other side be "b". According to the problem:
a + b = 10 cm
To find the area, we need the length of one of the sides. For simplicity, let's assume both sides are equal. Thus:
a = b = 10 cm / 2 = 5 cm
Calculating the Area
Now, substituting the values into the area formula:
Area = base × height
Area = 5 cm × 2 cm
Area = 10 cm²
Conclusion
The area of the parallelogram is 10 cm². Hence, the correct answer is option 'C'. This demonstrates how understanding the properties of parallelograms can help solve geometry problems effectively.
To find the area of a parallelogram, we can use the formula:
Area = base × height
Where:
- The base is the length of one of the parallel sides.
- The height is the perpendicular distance between the parallel sides.
Given Information
- The distance between the parallel sides (height) = 2 cm
- The sum of the lengths of the parallel sides = 10 cm
Finding the Base
Since we have the sum of the two parallel sides, we can define their lengths as follows:
Let one side be "a" and the other side be "b". According to the problem:
a + b = 10 cm
To find the area, we need the length of one of the sides. For simplicity, let's assume both sides are equal. Thus:
a = b = 10 cm / 2 = 5 cm
Calculating the Area
Now, substituting the values into the area formula:
Area = base × height
Area = 5 cm × 2 cm
Area = 10 cm²
Conclusion
The area of the parallelogram is 10 cm². Hence, the correct answer is option 'C'. This demonstrates how understanding the properties of parallelograms can help solve geometry problems effectively.
Top surface of a raised platform is in the shape of regular octagon as shown in the figure. Find the area of the octagonal surface.
- a)11.9 cm3
- b)119 cm
- c)119 m2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Top surface of a raised platform is in the shape of regular octagon as shown in the figure. Find the area of the octagonal surface.
a)
11.9 cm3
b)
119 cm
c)
119 m2
d)
None of these
|
Trisha Vashisht answered |
We will divide the octagon in 3 parts which are two trpeziums ABCH and DEFG and one rectangle CDGH and find the area for all of them separately and add them to get the area of octagon
If the above figure is a 3-D figure and seven spherical balls of radius 6 cm each are tightly arranged in a hexagonal box in a single layer, then what will be the volume of the box unoccupied by the balls in cm3?- a)3456√3+ 5184-252π
- b)3456√3+ 5184-288π
- c)576√3 +864-288π
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
If the above figure is a 3-D figure and seven spherical balls of radius 6 cm each are tightly arranged in a hexagonal box in a single layer, then what will be the volume of the box unoccupied by the balls in cm3?
a)
3456√3+ 5184-252π
b)
3456√3+ 5184-288π
c)
576√3 +864-288π
d)
None of these
|
|
Dipanjan Kulkarni answered |
The 3D shape of the hexagon will be a hexagonal prism.
What is the ratio of the number of unexposed smaller cubes to the total number of cubes?- a)1/27
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
What is the ratio of the number of unexposed smaller cubes to the total number of cubes?
a)
1/27
b)
c)
d)
|
|
Hridoy Mehra answered |
Take a value of n, say 3 and then check options.
A cube is inscribed in a hemisphere of radius R, such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the half-sphere. What is the volume of the cube?- a)0.25R3
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
A cube is inscribed in a hemisphere of radius R, such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the half-sphere. What is the volume of the cube?
a)
0.25R3
b)
c)
d)
|
|
Dipanjan Kulkarni answered |
Let ABCDEFGH be the cube of side a and O be the centre of the hemisphere.
AC = √2 a
OD = OC = R
Let P be the mid-point of AC
Let P be the mid-point of AC
OP = a
Now in Δ AOC
Three circles with radius 2 cm touch each other as shown :- 
- a)3π(4+√3)2
- b)π/2(4+2√3)2
- c)π/4(4+2√3)2
- d)12π−π/2(4+2√3)2
Correct answer is option 'B'. Can you explain this answer?
Three circles with radius 2 cm touch each other as shown :-
a)
3π(4+√3)2
b)
π/2(4+2√3)2
c)
π/4(4+2√3)2
d)
12π−π/2(4+2√3)2
|
|
Mainak Majumdar answered |
(This can easily be derived using trigonometry. However, please remember this formula. It is useful at places)
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