ShmoopTube

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Here’s a question that’s not particularly shmoopy…

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If the volume of a cube is 8 cubic inches, what is the surface area of the cube in square centimeters?

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And here are the potential answers...

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This question is testing, among other things, our sense of, well… common sense.

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So… we have this cube. We know its volume is 8 and that the formula for volume is

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base times width times height.

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So something times something times something is 8.

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And since it’s a cube we know that the numbers must all be the same so….. hint here...

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Yep, it’s gotta be the CUBE ROOT of 8 – or, said another way, the only answer that can

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make this work is if the sides of the cube are all of length 2 – 2 times 2 times 2 is… 8.

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OK, so we know the size of the cube we’re dealing with.

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But ah, the twist – the question is asking for the answer in square centimeters – not inches.

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And since we know that each of its sides are 2 inches long, we can just convert these to centimeters now.

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1 inch equals approximately 2.5 centimeters, so each side length of the cube is 5 centimeters.

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We can multiply base times width to get the area of each face of the cube, which is just

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5 times 5 here and here… to get an area of 25 square centimeters.

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And lastly, note that we have 6 surfaces on the cube – each surface has area 25 –

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…multiply them (6 x 25) and we get 150 total square centimeters of surface area.

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Which gives us answer C.

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Ok… here's something tricky though.

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If we had solved through to the surface area of the cube in inches and then converted to

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centimeters afterwards, it's actually a bit different.

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Let's say we used the 2 inch side lengths, multiplied base times width to get the area

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of each face of the cube which is just 2 x 2 here to get an area of 4 square inches...

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…and then multiplied by 6 to get a total of 24 total square inches of surface area.

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The trick here is that we can't just multiply 24 by 2.5, because even though 1 inch equals

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2.5 centimeters, 1 SQUARE inch doesn't equal 2.5 centimeters...

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…it equals the quantity 2.5 centimeters SQUARED...2.5 squared equals 6.25.

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We can then take 24 times 6.25, which equals 150 square centimeters.

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But what do you know… looks like we got C again.

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So we won’t have to take this thing to a higher court.

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