Volume of Regular Pyramids

Q.

Find the volume of prism

Q.

Question 2

A rectangular piece of dimensions 3 cm x 2 cm was cut from a rectangular sheet of paper of dimensions 6 cm x 5 cm (see the figure). Area of remaining sheet of paper is


(a) $30c{m}^2$
(b) $36c{m}^2$
(c) $24c{m}^2$
(d) $22c{m}^2$

Q.

The volume of square pyramid of base edge 5 m and height 12 m is (in cubic centimetres) :

1. 75

2. 100

3. 90

4. 64

Q. Question 3
A cistern measuring $150cm\times 120cm\times 110$ cm has $129600c{m}^3$ water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being $22.5cm\times 7.5cm\times 6.5cm?$

Q.

The ratio between the base edges of two square pyramids is 1:4. If the heights are also in the same ratio and the volume of the second pyramid is 400 cubic centimetres, what is the volume of the first square pyramid?

1. $16cubiccentimetres$

2. $6.25cubiccentimetres$

3. $4cubiccentimetres$

4. $20cubiccentimetres$

Q. The slant height of a square pyramid is 10 cm and its surface area is 144 square centimetres. What is the volume of the square pyramid?

1. $384cubiccentimetres$
2. $100cubiccentimetres$
3. $400cubiccentimetres$
4. $192cubiccentimetres$

Q. If the height and the slant height of a square pyramid are $8cm$ and $10cm$ respectively, what is the volume of the pyramid?

1. $192cubiccentimetres$
2. $120cubiccentimetres$
   
3. $384cubiccentimetres$
4. $96cubiccentimetres$
   

Q. Match the following for a square pyramid with base edge length 24 cm, and height 16 cm.

1. $960c{m}^2$
2. $1536c{m}^2$
3. $3072c{m}^3$

Q. The height of a square based pyramid of volume $300$c.c is $10$cm. Find the edge of the base.

Q. The volume of a rectangular box (or cuboid) whose length, breadth and height are 7 cm, 3 cm and 3 cm respectively, is.

1. $49c{m}^3$
2. $63c{m}^3$
3. $81c{m}^3$
4. $100c{m}^3$

Q.

Visualise the area of a cuboid.

Q. The height of a square based pyramid is $33$cm. If the length of the base is $27$cm, find the volume.

Q.

A prism is completely filled with $80$ cubes that have an edge length of $12$ cm.

What is the volume of the prism?

Q.

Sonu was making sand pyramids at the beach. He designed his pyramids with a base edge of 10 cm and height 33 cm. He would go collect wet sand with his small cylindrical bucket of radius 5 cm and 7 cm height. How many times does he need to collect the wet sand in order to construct his sand pyramid?

1. Surface area of cone = Surface area of sphere

2. Radius of cone = Radius of Radius of sphere

3. Height of cone = Height of cylinder

4. Volume of cone = volume of sphere

Q. Consider a pyramid with a square base side of $6$ inches and with a height of $12$ inches, as shown below. If we cut off the top of the pyramid parallel to the base $3$ inches from the tip, what is the volume of the remaining solid?

1. $141.75$
2. $140$
3. $135.48$
4. $144$
5. $130$

Q.

Nidhi constructed a square pyramid of base edge 10cm and height 6cm. Rahul made a square pyramid of base edge 5cm and height 24cm. What is the ratio of the volumes of the pyramids constructed by Nidhi and Rahul?

1. 1:1

2. 1:2

3. 2:1

4. 1:4

Q. If base and height of a prism and pyramid are same, then the volume of a pyramid is:

1. $3\times$ Volume of prism
2. $\frac{1}{2}\times$ Volume of prism
3. $\frac{1}{3}\times$ Volume of prism
4. $2\times$ Volume of prism

Q. The length of the base of a square pyramid is $2cm$ and the height is $6cm$. Calculate the volume.

1. $8c{m}^3$
2. $6c{m}^3$
3. $4c{m}^3$
4. $2c{m}^3$

Q. A regular square pyramid is $3m$. height and the perimeter of its base is $16m$. Find the volume of the pyramid.

Q. Each side of the base of a square pyramid is reduced by $20$. By what percent must the height be increased so that the volume of the new pyramid is the same as the volume of the original pyramid?

1. 20
2. 40
3. 56.25
4. 46.875
5. 71.875

Q.

A right triangular prism has a height of $26\mathrm{cm}$ and base edges of $10\mathrm{cm},24\mathrm{cm},$ and $26\mathrm{cm}$.

What is the lateral area of the prism?

1. $1560{\mathrm{cm}}^2$

2. $1680{\mathrm{cm}}^2$

3. $800{\mathrm{cm}}^2$

4. $3120{\mathrm{cm}}^2$

Q. If the area of base of a rectangular based pyramid is $60m^2$ and its height is $7.5$ m, find the volume.

Q.

Which of the following represents the volume of a pyramid?

1. $\frac{1}{3}\times \text{Base area}\times \text{Slant height}$

2. $\frac{1}{3}\times \text{Base area}\times \text{Height}$

3. $\frac{1}{3}\times \text{Base edge}\times \text{Slant height}$

4. $\frac{1}{3}\times \text{Base edge}\times \text{Height}$

Q.

Find the volume of the square pyramid, if one the triangular faces is given below.

1. 20

2. 50

3. 40

4. 30

Q. The base of the right pyramid is a square of side 16 cm and height 15 cm. Its volume $\left(c{m}^3\right)$ will be

1. $3840$
2. $1280$
3. $960$
4. $1920$

Q.

A steel beam that is 12 meters long is cut into four equal parts. The cross sections are rectangles with side lengths of 1 meter and 2 meters.

(c) What is the volume of the original beam?

Q.

If the height of a square pyramid is 10 m and its base edge is 12 m long, then find its volume.

1. $840m^3$

2. $480m^3$

3. $408m^3$

4. $48m^3$

Q. If a regular square pyramid has a base of side $8cm$ and height of $30cm$, then its volume is

1. $640c{m}^3.$
2. $240c{m}^3.$
3. $120c{m}^3.$
4. $900c{m}^3.$

Q. Consider that the base of a square pyramid is equal to the length of side of cube. Then $\frac{\text{Volume of Cube}}{\text{Volume of Square Pyramid}}=$

Q. A square pyramid is inscribed in a cube of total surface area of $24$ square cm such that the base of the pyramid is the same as the base of the cube. What is the volume of the pyramid?

1. $\frac{1}{3}$
2. $\frac{8}{3}$
3. $6$
4. $4$
5. $8$