1951 AMC 12 Problem 4

Attempt Problem 4 of the 1951 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 1951 AMC 12 solutions, or check the answer key.

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

4.

A barn with a flat roof is rectangular in shape, 1010 yd. wide, 1313 yd. long, and 55 yd. high. It is to be painted inside and outside, and on the ceiling, but not on the roof or floor. The total number of square yards to be painted is:
360360
460460
490490
590590
720720
Answer: D
Concepts:rectangular prismsurface area
Small hint:
Count both the inside and outside faces of each of the four walls
Big hint:
The ceiling contributes one 1010-by-1313 rectangle
Solution:
The four walls have one-sided area 2(13⋅5)+2(10⋅5)=230. 2(13\cdot5)+2(10\cdot5)=230. Painting them inside and outside contributes 2(230)=460.2(230)=460. The ceiling adds 10⋅13=130,10\cdot13=130, so the total is 460+130=590.460+130=590.
Thus, the correct answer is D.
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