Solid geometry is concerned with three-dimensional shapes.

In these lessons, we will learn

### What is Volume?

### Volume of a Cube

**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.### Word Problems about Cubes

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

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.

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}

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 = *s ^{3}*

Since the cube has six square-shape sides, the

Surface area of a cube = 6*s*^{2}

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.

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?

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
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