Class 8 Maths Mensuration | Volume of Cube, Cuboids and Cylinder |

__Volume of Cube, Cuboids and Cylinder__

Amount of space occupied by a three dimensional object is called its volume.

**Cube:**

The cube is a special case of a cuboid, where l = b = h.

Hence, volume of cube = l * l * l = l^{3}

__Problem:__ Find the volume of cube if its each side is of length is 5 cm.

Solution:

Given, l = b = h = 5 cm

volume of cube = l * b * h = 5 * 5 * 5 = 125 cm^{3}

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**Cuboid:**

Volume of a cuboid is equal to the product of length, breadth and height of the cuboid.

Let l is the length, b is the breadth and h is the height of the cuboid.

Then volume of cuboid = l * b * h

__Problem:__ Find the height of a cuboid whose base area is 180 cm^{2} and volume is 900 cm^{3}?

Solution:

Given: Base area of cuboid = 180 cm^{2} and Volume of cuboid = 900 cm^{3}

We know that, Volume of cuboid = l * b * h

=> 900 = 180 * h [Base area = l * b = 180 (given)]

=> h = 900/180

=> h = 5 m

Hence, the height of cuboid is 5 m.

**Cylinder:**

Let r is the radius of circular region and h is the height of cylinder.

Then volume of cylinder = πr^{2} * h = πr^{2}h

__Problem: __Find the height of the cylinder whose volume if 1.54 m^{3} and diameter of the base is 140 cm.

Solution:

Given: Volume of cylinder = 1.54 m^{3} and Diameter of cylinder = 140 cm

Radius (r) = 140/2 = 70 cm

Volume of cylinder = πr^{2} h

=> 1.54 = 22/7 * 0.7 * 0.7 * h

=> 1.54 = 22 * 0.1 * 0.7 * h

=> 1.54 = 1.54 * h

=> h = 1.54/1.54

=> h = 1 m

Hence, the height of the cylinder is 1 m.

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