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Question on a solid cube

This topic has 1 expert reply and 0 member replies

Question on a solid cube

Post Fri Oct 21, 2016 11:29 am
Hello,

Would be thankful if you could please provide an elaborate explanation of the attached question on geometry.

Obliged, Sucheta
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Post Fri Oct 21, 2016 4:07 pm
This is a GRE question, not a GMAT question. Technically, you should not be posting those here.

While the two tests are largely similar in the quant content that they test, the structures of the questions are quite different. So, I will not provide a solution to the actual question here, but I will explain the content generally.

If we want to find the surface area of a rectangular solid (L*W*H), we want to think of each face as an individual rectangle:
an L*W rectangle... plus another identical one on the opposite side.
an H*L rectangle... plus another identical one on the opposite side.
an H*W rectangle... plus another identical one on the opposite side.

So the total surface area = 2(LW + HL + HW)

For each individual rod in the diagram, we can infer that the dimensions are 6*1*1 (width and height both divided into 3 equal parts).
Surface area = 2(6*1 + 6*1 + 1*1) = 2(13) = 26

For the entire figure, the dimensions are 6*3*3.
Surface area = 2(6*3 + 6*3 + 3*3) = 2(18 + 18 + 9) = 2(45) = 90

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