# Surface Area of a Cube

Good thing surface areas are as easy as they seem on the surface.

Basic Geometry | Area and Volume |

Language | English Language |

Solid Geometry | Surface Area |

### Transcript

...how much material will he need to make a perfect-fitting box cozy?

We can use the cube's volume to help Harold figure out its surface area.

Here are our choices:

First, let's break down that box. We can start by working backwards.

We know that the volume of our cube is 1,728. So now we need to work backwards.

Volume is length times width times height.

Lucky for us, all are the same length in a cube.

To find volume, we can raise length, width or height to the third power... or cube it.

So we simply need to take the cube root of the volume.

The cube root of 1,728 is 12.

There's our length, width and height.

Now let's find the surface area of one side.

Multiply the box's width by its height.

So that is 12 times 12, which gives us 144... How many sides are there again, Harold?

Yep... six of 'em.

So 144 times 6 equals... 864.

Choice E, you're the winner!

Now Harold has enough material to hide his home...

...and doesn't have to worry about some box-thief filching it in the night.

Sleep tight, Harold. Don't let the literal bed bugs bite.