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

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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 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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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