# Volume Enclosed By A Cube

## Definition:

The number of cubic units that will exactly fill a cube.

How to find the volume of a cube?

Recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. So if the length of an edge is 4, the volume is 4 x 4 x 4 = 64

Or as a formula:

volume = s3, where: s is the length of any edge of the cube.

In the figure above, drag the orange dot to resize the cube. From the edge length shown, calculate the volume of the cube and verify that it agrees with the calculation in the figure.

When we write **volume = s**^{3}, strictly speaking this should be read as "s to the power 3", but because it is used to calculate the volume of cubes it is usually spoken as "s cubed".

**Volume:** The volume of a three-dimensional shape is a measurement of the space occupied by the shape.

Volume is measured in cubic units.

The volume of a unit cube

= 1 unit × 1 unit × 1 unit

= 1 unit^{3} ( Read as one cubic unit )

The volume of a cube with sides 1 cm × 1 cm × 1 cm

Volume = 1 cm × 1 cm × 1 cm = 1 cm^{3} ( Read as one cubic cm )

Some important units of conversion for volume are:

1 cm^{3} = 1,000 mm^{3}

1 m^{3} = 1,000, 000 cm^{3}

## Volume of a Cube

A cube is a three-dimensional figure with six matching square sides.

The figure above shows a cube. The dotted lines indicate edges hidden from your view.

If s is the length of one of its sides, then the volume of the cube is *s* × *s* × *s*

Volume of the cube = s^{3}

Since the cube has six square-shape sides, the Surface area of a cube = 6s^{2}