ShmoopTube

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Here’s your shmoop du jour, brought to you by a box that is two-thirds full.

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Or, as we might look at it depending on our mood…one-third empty.

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A rectangular box with a square base and a height of twice the length of the base, is

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to be filled two-thirds of the way full. If x is the length of one side of the base,

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what is the volume of the remaining space in the box?

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Here are the potential answers...

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Okay, so we’re not sure what exactly this box is filled with…

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...all we know is that we recently saw someone carrying it out of the horses’ stable.

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So…we’re not gonna ask. All right, now let’s picture this box.

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Square base… but with a height twice the length of the base.

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And it’s filled 2/3 of the way with… something.

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We want to determine how much room we have leftover.

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We’re calling a length of the square base “x”…

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…and since we know the sides are twice as long as the base, we can call the height “2x.”

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Now for the volume portion of the program…

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We need to take length times width times height to get the volume.

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Since we know the base is a square, both of those measurements are just…”x.”

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So to find the volume, we take x times x times 2x…

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…to get 2x cubed. But that’s the total volume of the box.

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If only 1/3 of that is empty space…

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…then we take 1/3 times 2x cubed to get 2/3x cubed…

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…which is answer B.

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We love problems like this. They really… fertilize the imagination…

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