Volume of a Prism

Q. The areas of three adjacent faces of a cuboid are x, y, z .the volume is V , prove that V square = xyz

Q.

The base of a prism is an equilateral triangle of perimeter 15 centimetres and its height is 5 centimetres. What is its volume?

Q.

A cylinder of base diameter 8cm and height 7cm is dipped vertically one third in a bucket full of paint. How much area gets painted?

Q. Derivation of volume and total surface area of cube cuboid and pyramid

Q.

MODELING REAL LIFE A battery for an underwater drone is in the shape of a square prism. It is designed to draw in seawater that is then used to produce energy. The base of the battery has side lengths of 15 centimeters and the height of the battery is 10 centimeters. Find the volume of the battery.

Q.

The perimeter of the base of an equilateral triangular prism is 30 cm. The height of the prism is 17 cm. The volume of the prism is _______

1. $415\sqrt{3}c{m}^3$

2. $435\sqrt{3}c{m}^3$

3. $525\sqrt{3}c{m}^3$

4. $425\sqrt{3}c{m}^3$

Q.

The volume of a square pyramid of base edge 12 cm and height 18 cm is:

1. 864

2. 932

3. 664

4. 728

Q. A prism has an equilateral triangular base. The side of the triangle is 8 cm, and the height of the prism is 14 cm. Find the volume of the prism in cc.

1. 384

Q.

A vessel is in the shape of a square prism, with each side of the base 16 centimetres long. It contains water 10 centimetres high. If a cube of side 8 centimetres is completely immersed in it, how high would the water level rise?

Q. The base area of a prism is $60c{m}^2$. Find the height of the prism if its volume is $540c{m}^3$.

1. 9

Q. The length of the longest rod that can fit in a cubical vessel of side 10 cm, is
(a) 10 cm
(b) 20 cm
(c) $10\sqrt{2}\mathrm{cm}$
(d) $10\sqrt{3}\mathrm{cm}$

Q.

A triangular prism has an equilateral triangular base. The side of the triangle is 8 cm and the height of the prism is 14 cm. What is the volume of the triangular prism?

1. $204\sqrt{3}c{m}^3$

2. $234\sqrt{3}c{m}^3$

3. $214\sqrt{3}c{m}^3$

4. $224\sqrt{3}c{m}^3$

Q.

The volume of a square prism is 3600 cubic centimetres and its base area is 144 square centimetres. What is its surface area?

Q. The base of a prism is an equilateral triangle of perimeter 15 cm and the height is 5 cm. Find the volume of the prism.

Q.

A hexagonal tank has sides of its base as 4 m each. The height of the tank is 10 m. Find the volume of the water tank.

1. $240\sqrt{3}{m}^3$
2. $230\sqrt{3}{m}^3$
3. $250\sqrt{3}{m}^3$
4. $260\sqrt{3}{m}^3$

Q.

If the areas of the adjacent faces of a rectangular block are in the ratio of 2:3:4 and it's volume is 9000 cm³ , then what is the length of the shortest side? And is the longest side as well?

Q. Volume of a hexagonal prism whose base area is $40c{m}^2$ and height is 35 cm is .

1. $1000c{m}^3$
2. $1600c{m}^3$
3. $1400c{m}^3$

Q.

Find the surface area of the prism or regular pyramid.

Q. Find the volume of a hexagonal prism whose base area is $40c{m}^2$ and height is $35cm$ in $c{m}^3$.

1. 1400

Q.

Find the surface area of the prism or regular pyramid:

Q.

Find the volume of hexagonal prism whose base area is $40c{m}^2$ and height is 35 cm.

1. $1000c{m}^3$

2. $1600c{m}^3$

3. $1400c{m}^3$

4. $1200c{m}^3$

Q. A hexagonal tank has sides of its base as 4 m each. The height of the tank is 10 m. Find the volume of the water tank.

Q.

A roof is made by using 20 triangular rocks which includes 4 different colors. The sides of each piece are 2m, 5m and 5m. How much area is covered by the colored rocks?

1. 2

2. 20

3. 6

4. 25

Q. If the volume of a prism is 128 cc and the base area is 16 sq. cm, then find its height.

1. 8 cm
2. 4 cm
3. 13 cm
4. 12 cm

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. Volume of a prism can be obtained by multiplying the area of it's base and height.

1. True
2. False

Q.

Two identical prisms with triangles as base are joined to form a rectangular prism as shown below.

What is the total surface area of the rectangular prism?

Q. If the volume of a square prism is 27 cubic units, find its length.

1. 2
2. 5
3. 3
4. 4