ShmoopTube

00:03

Here’s your shmoop du jour, brought to you by a red box.

00:08

If you’d like to watch an entire movie about it… we suggest you visit your local Redbox.

00:15

Sierra is painting all of the visible surfaces of a box red.

00:19

The sides and the entire inside will be painted, including the bottom inside.

00:24

There is no top and the bottom outside of the box will not be painted.

00:28

One jar of paint will cover an area of 2x2 units.

00:32

How many jars of paint will Sierra need?

00:35

Here are the potential answers...

00:38

First of all, what exactly is Sierra going to be painting?

00:43

That part is a little wordy…but it’s basically just saying that she needs to paint everything

00:47

we can see in this diagram.

00:50

All four sides, inside and out, and the bottom inside… but not the part that’s resting on the ground.

00:59

We have two long sides, but four long surfaces, each with a length of 2x and a height of 0.5x.

01:06

4 times 2x times 0.5x is 4x squared. On to the short sides.

01:13

Same deal, except the length is now just x. 4 times x times 0.5x is 2x squared.

01:19

Finally, we’ve got the inside bottom – only one surface.

01:22

It’s just x times 2x… or 2x squared. Adding them up, we have 4x squared plus 2x

01:29

squared plus 2x squared… …or 8x squared.

01:33

Okay, so that’s our total area… but what does that number mean for us?

01:37

One jar of paint covers only 2x squared units…

01:40

We take 8x squared divided by 2x squared…which is 4.

01:44

So our answer is option C.

01:46

Unfortunately, Sierra’s older sister tried to steal the box…

01:49

but don’t worry. We caught her red-handed.

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