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You look like you could use a shmoopy question…

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Ivan is a Russian bartender with a particular affinity for nesting dolls.

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He wants to apply the same idea to ice cubes.

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The guy dreams big, what can we say?

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In the figure below, how many of the 3 inch

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cubes would fit into a rectangular block of ice with the dimensions as shown?

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And here are the potential answers...

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Tons of things going on here so let’s start by just standardizing units.

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That is, making everything into inches instead of feet.

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We can glean that the ice cube in the upper corner of the larger block of ice there is

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one FOURTH of the way across because it is labeled 3 inches…

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…and you can see that the front base is a foot – 12 inches.

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Now since it’s an ice cube, the CUBE being the operative word here,

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by definition all sides are the same length.

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So this line is 3 inches as well and the side length of the bigger block of ice

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is 1 and a quarter feet, or 15 inches.

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The back side is 1 and a half feet, or 18 inches.

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So let’s calculate the volume of the rectangular ice block by multiplying base times width

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times height – all in inches - and we get 12 times 15 times 18 is 3,240.

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So the volume of the rectangular block is 3,240 cubic inches.

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Now we have to figure out how many 3 by 3 inch cubes can fit in there.

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Well, the volume of these cubes is calculated the same way as the larger ice block –

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base times height times width.

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We have 3 times 3 which is 9… times 3 which is 27.

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So to figure out how many cubes should fit into the larger chunk of ice, we divide 3,240 by 27...

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Okay, there we go. And we get 120. The answer is D.

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As in, “Don’t quit your day job.”

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