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Volume of a Cube

A cube has all 6 faces as squares. As we saw earlier, the volume of a prism is calculated by multiplying the area of the cross-section by its perpendicular height (or length or depth).

volume of a cube_1In a cube, the area of the cross-section is the area of a square face and the height of the cube is the side length of the square.

Here the area of cross-section (shaded area) = area of square

  = a × a = a²

The height of the cube is side length of the square = a. Hence,

Volume of a cube = area of cross-section × perpendicular height

= a² × a = a³

Volume of a cube V = a³ or (side)³

In other words, to find the volume of a cube, we cube the side length or multiply the side by itself thrice.

Let us look at a few examples of calculating the volume of a cube:

volume of a cube_2Example 1: Find the volume of the cube shown here.

Volume of a cube = Area of cross-section × height

V = A × h

Area of cross-section (square) = 2 × 2 = 4 cm²

And perpendicular height = 2 cm

V = 4 × 2 = 8 cm³


volume of a cube_3Example 2: Find the volume of cube with side length 5 cm.

We can calculate the area using the two step process of first finding the area of of cross-section, and then multiplying this area by the height.

Instead, we would use the formula straight away as

V = (side)³ to calculate the volume of a cube.

V = (5)³

= 5 × 5 × 5

= 125 cm³


Example 3: Calculate the volume of a cube with side length 4.2 mm to 1 decimal place.

Volume = (side)³

= (4.2)³

= 4.2 × 4.2 × 4.2

= 74.088

= 74.1 mm³