Volume of a Cube

Solid geometry is concerned with three-dimensional shapes. In this lesson, we will learn

• what is volume?
• how to find the volume of a cube.
• how to solve word problems about cubes.
• about nets of a cube.

What is 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 unit³ ( 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 cm³ ( Read as one cubic cm )

Some important units of conversion for volume are:

1 cm³ = 1,000 mm³

1 m³ = 1,000, 000 cm³

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 = s³

Since the cube has six square-shape sides, the

Surface area of a cube = 6s²

Worksheet to calculate volume and surface area of cubes.

The following videos show how to find the volume of a cube.

Word Problems about Cubes

This video gives a word problem about cubes.

A shipping company fills cases with boxes that are cubes. They pack 20 boxes of cubes in a case. What are the possible dimensions of the case?

Nets of a Cube

Imagine making cuts along some edges of a cube and opening it up to form a plane figure. The plane figure is called the net of the cube. There are 11 possible nets for a cube as shown in the following figures.

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