1959 AMC 12 Problem 1

Attempt Problem 1 of the 1959 AMC 12 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 1959 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

Each edge of a cube is increased by 50%.50\%. The percent of increase of the surface area of the cube is:
5050
125125
150150
300300
750750
Answer: B
Concepts:percentagesurface areapower scaling of length, area, and volume
Small hint:
Compare the new edge length with the old edge length
Big hint:
Surface area changes by the square of the linear scale factor
Solution:
If the original edge length is s,s, the new edge length is 1.5s.1.5s. Thus the surface area is multiplied by (1.5)2=2.25. (1.5)^2=2.25. The increase is 1.251.25 times the original area, or 125%.125\%.
Thus, the correct answer is B.
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