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A large cube is composed of smaller cubes, each of which are

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A large cube is composed of smaller cubes, each of which are [#permalink] New post 27 Mar 2018, 21:52
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A large cube is composed of smaller cubes, each of which are 125 cubic centimeters in volume. If the larger cube has four of these smaller cubes as one of its lengths, what is the total volume of the larger cube, in cubic centimeters?

A)125
B)625
C)2,000
D)8,000
E)15,625
[Reveal] Spoiler: OA
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Re: A large cube is composed of smaller cubes, each of which are [#permalink] New post 29 Mar 2018, 18:47
Firstly, let's figure out the side length of the smaller cubes. Since they have a volume of 125, and the formula for volume of a cube is V = s^3 (where s is the length of the sides) we know that the sides of the small cubes are 5. (This is because we recognize 125 as 5 cubed.)

Now, since the large cube has 4 small cubes to a side, we know the sides of the large cube are 20. Reapplying the volume formula, the volume of the large cube should be 20 cubed. The easiest way to do this arithmetic is to think of the 20 as 2x10 and cube them separately. Since 2 cubed is 8, and 10 cubed is 1000, we can multiply the two to get 20 cubed, getting us 8000. So the answer is D.
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Re: A large cube is composed of smaller cubes, each of which are   [#permalink] 29 Mar 2018, 18:47
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