ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Surface Area of a Cube 5080 Views


Share It!


Description:

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

Language:
English Language

Transcript

00:06

Surface of a Cube, a la Shmoop. Harold the hobo would like to cover his new

00:12

box while he sleeps at night...

00:14

...so no one sees it and tries to steal it.

00:18

Harold's not the smartest knife in the drawer. Man, he sure wishes he had a drawer.

00:23

Assuming Harold knows the volume of the cube is 1,728 milliliters...

00:27

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

00:32

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

00:37

Here are our choices:

00:39

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

00:46

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

00:51

Volume is length times width times height.

00:54

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

00:57

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

01:04

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

01:07

The cube root of 1,728 is 12.

01:18

There's our length, width and height.

01:22

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

01:25

Multiply the box's width by its height.

01:27

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

01:34

Yep... six of 'em.

01:37

So 144 times 6 equals... 864.

01:42

Choice E, you're the winner!

01:44

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

01:48

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

01:59

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

Up Next

Surface Area of Cylinders
14740 Views

Haven't you always wondered how much cardboard it takes to encase a trunk warmer for your pet elephant?

Related Videos

Geometría 3D
207 Views

Es una cosa cuando todas esas figuras geométricas están puestas en un pie de la página, pero cuando estas empiezan a expanderse y a invader nues...

An Introduction to 3D Geometry
812 Views

Does thinking about 3D Geometry get you bent out of shape? Never fear! Watch this video and figure out some fun new shapes to bend back into. We're...

ACT Math 1.5 Plane Geometry
295 Views

ACT Math: Plane Geometry Drill 1, Problem 5. If two polygons have the same shape and size, they are what?