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}

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

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