# Volume of a Cube

In these lessons, 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.

Solid geometry is concerned with three-dimensional shapes and their properties.

### 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 equal edges and 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.

How to find the volume of a cube?

Step 1: Find the length of a side
Step 2: Substitute into the equation
Step 3: Evaluate
Step 4: Write the units

Find the volume of a cube with side length of 20 feet.

This video gives a word problem about the volume of cubes.

Example:
Alex formed the solid as shown below. It is made up of 2-in cubes. What is the volume of the solid?

Example:
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. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 