2000 AMC 8 Problem 22
Attempt Problem 22 of the 2000 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2000 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
22.
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
Answer: C
Small hint:
The original cube has surface area
Big hint:
The small cube hides one unit square but adds five
Solution:
The original surface area is just
Note that the top face of the unit cube plus the visible area of the top face of the larger cube is the same as the area of one face of the larger cube.
This means that the unit square on top only adds unit squares to the total surface area, making the increase
The percent increase is therefore
Thus, C is the correct answer.
Problem 22 in other years
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