Problem:
A cube has edge length . Suppose that we glue a cube of edge length on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to:
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Answer Choices:
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Solution:
The area of each face of the larger cube is . There are six faces of the cube, so its surface area is . When we add the smaller cube, we decrease the original surface area by , but we add units of area unit for each of the five unglued faces of the smaller cube), This is a net increase of from the original surface area, and is of . The closest value given is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions