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You look like you could use a shmoopy question… Ivan is a Russian bartender with a particular
affinity for nesting dolls. He wants to apply the same idea to ice cubes.
The guy dreams big, what can we say? In the figure below, how many of the 3 inch
cubes would fit into a rectangular block of ice with the dimensions as shown?
And here are the potential answers: Tons of things going on here so let’s start
just by standardizing units.
That is, making everything into inches instead of feet.
We can glean that the ice cube in the upper corner of the larger block of ice there is
one FOURTH of the way across because it is labeled 3 inches…
…and you can see that the front base is a foot – 12 inches.
Now since it’s an ice cube, the CUBE being the operative word here, by definition all
sides are the same length.
So this line is 3 inches as well and the side length of the bigger block of ice is 1 and
a quarter feet, or 15 inches.
The back side is 1 and a half feet, or 18 inches.
So let’s calculate the volume of the rectangular ice block by multiplying base times width
times height – all in inches - and we get 12 times 15 times 18, or 3,240.
So the volume of the rectangular block is 3,240 cubic inches.
Now we have to figure out how many 3 by 3 inch cubes can fit in there.
Well, the volume of these cubes is calculated the same way as the larger ice block – base
times height times width.
We have 3 times 3 which is 9… times 3 which is 27.
So to figure out how many cubes should fit into the larger chunk of ice, we divide 3,240
by 27 and we get…
120. The answer is D.
As in, “Don’t quit your day job.”