VOLUME OF A CUBOID

VOLUME OF A CUBOID

The volume of a cuboid is simply the space occupied by it. A cuboid is a three-dimensional shape that has rectangles as its faces. It has a length, breadth and height. It has 6 faces and the opposite faces of a cuboid are equal. The volume of a cuboid is  (length x breadth x height).

DERIVATION OF THE FORMULA OF VOLUME OF A CUBOID

It is easy to derive the formula of a volume of a cuboid. Consider a rectangular sheet of paper of length ‘l’ millimetre and breadth ‘b’ millimetre. Now, let us stack such 50 sheets on top of each other and form a pile. If each sheet is 1 millimetre thick, then after piling 50 such sheets, the height of the pile becomes 50 millimetres.

The volume of the cuboid formed can be simply interpreted as the space occupied by the pile of sheets with length ‘l’, breadth ‘b’ and height 50 millimetres.

Therefore, the formula for the volume of a cuboid is( length x breadth x height).

Also, it is important to note that the unit of the volume is unit³

Let us solve a few problems

Q1. The length of a cuboidal box is 15 cm with a breadth of 10 cm. The height of the cuboid is 100 mm. Calculate the volume of the box?

Ans: The height of the cuboid is in millimetres so we will first convert it to cm to make our calculations possible.

Height = 100 m = 100/10 = 10 cm

Length = 15 cm

Breadth = 10 cm

Volume = length x breadth x height

Volume = 15 x 10 x 10 = 1500 cm³

Q2. Suppose that the volume of a cuboid is 3000 inch³ . The length is 10 inches and the breadth is 15 inches. Find its height.

Ans. Volume = length x breadth x height

3000 = 10 x 15 x h

3000/150 = h

20 = height