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).
In 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:
Example 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
Example 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 × 4.2 × 4.2
= 74.1 mm³