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GMAT Prep
Conveyer Belt.jpg
As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?
A. (15−π)/2
B. (5π)/4
C. 15−2π
D. 15−π
E. 2π
OA
A
We should first note that the conveyor belt can be decomposed into two semicircular pieces, each of which has radius 0.5 meters, and two straight pieces, each of which has a length equal to the length between the centers of the two wheels.
Since each wheel has a radius of 0.5 meters, we know that the circumference of each wheel is 2 x π x 0.5 = π meters. Since the belt goes around half of each circle, a length of π/2 meters of the belt goes around each circle. However, since there are two circles, a length of 2 x π/2 = π meters of the belt goes around the two semicircles.
The entire belt is 15 meters long, so the two straight pieces of the belt have a combined measure of (15 - π), which means the distance between the centers of the circles is (15 - π)/2.
Answer: A
Scott Woodbury-Stewart
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