ShmoopTube

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

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box while he sleeps at night...

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

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

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

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

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

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Here are our choices:

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

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

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Volume is length times width times height.

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

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

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

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The cube root of 1,728 is 12.

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There's our length, width and height.

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

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Multiply the box's width by its height.

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

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Yep... six of 'em.

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So 144 times 6 equals... 864.

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Choice E, you're the winner!

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

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

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

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