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 = l3

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 cm3

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 cm2 and volume is 900 cm3?

Solution:

Given: Base area of cuboid = 180 cm2 and Volume of cuboid = 900 cm3

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 = πr2 * h = πr2h

Problem: Find the height of the cylinder whose volume if 1.54 m3 and diameter of the base is 140 cm.

Solution:

Given: Volume of cylinder = 1.54 m3 and Diameter of cylinder = 140 cm

Radius (r) = 140/2 = 70 cm

Volume of cylinder = πr2 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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