Related Topics: More Geometry Lessons

In these lessons, we will learn

### Surface Area of a Cube

A cube is a three-dimensional figure with six equal square faces.

The surface area of a cube is the sum of the area of the six squares that cover it.

The following figure shows the surface area of a cube. Scroll down the page for more examples and solutions of finding the surface area of a cube.

*s*^{2} = 6(3)^{2} = 54 cm^{2}

**How to find the surface area of a cube?**

**Example:**

Given a side of 3 cm, find the surface area of the cube.** How to find the surface area of a cube?**

Step 1: Find the length of a side

Step 2: Substitute into the formula: side × side × 6 and evaluate

Step 3: Write the units**How to find the length of a cube given the surface area?**

This video shows how to find the length of a cube given the surface area.

Example: The total surface area of a cube is 216 in^{2}. What is the length of each side of the cube?
**How to use the net of a cube to find its surface area?**

**How to use nets and 3-dimensional figures to find surface area of cubes and prisms?**
**Surface Area of a Cube in terms of its Volume**

How to find the surface area of a cube in terms of volume

S = 6V^{2/3}

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

- how to calculate the surface area of a cube.
- how to find the length of a cube given the surface area.
- how to use the net of a cube to find its surface area.
- how to find the surface area of a cube in terms of its volume.

The surface area of a cube is the sum of the area of the six squares that cover it.

The following figure shows the surface area of a cube. Scroll down the page for more examples and solutions of finding the surface area of a cube.

If *s* is the length of one of its sides, then the area of one face of the cube is *s*^{2.}

Since a cube has six faces the surface area of a cube is six times the area of one face.

Surface area of a cube = 6

s^{2}

Worksheet to calculate volume and surface area of cubes

**Example**

Find the surface area of a cube with a side of length 3 cm

**Solution:**

Given that *s* = 3

Given a side of 3 cm, find the surface area of the cube.

Step 1: Find the length of a side

Step 2: Substitute into the formula: side × side × 6 and evaluate

Step 3: Write the units

This video shows how to find the length of a cube given the surface area.

Example: The total surface area of a cube is 216 in

Another way to look at the surface area of a cube is to consider a net of the cube. The net is a 2-dimensional figure that can be folded to form a 3-dimensional object.

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.

The following net can be folded along the dotted lines to form a cube.

We can then calculate the area of each square in the net and then multiply the area by 6 to get the surface area of the cube.

There are altogether 11 possible nets for a cube as shown in the following figures. Notice that the surface area of each of the net is the same.

How to find the surface area of a cube in terms of volume

S = 6V

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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