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Geometry and Measurement Videos 48 videos

SAT Math 3.3 Geometry and Measurement
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SAT Math 3.3 Geometry and Measurement

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SAT Math 6.1 Geometry and Measurement

SAT Math 4.2 Geometry and Measurement
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SAT Math 4.2 Geometry and Measurement

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Surface Area of a Cube 5082 Views


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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.

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