As shown in the figure above, a thin conveyor belt 12 meters long is drawn tightly around two circular wheels each 0.5 meters in radius. What is the distance, in meters, between the centers of the two wheels?


A. \(2\pi\)

B. \(\frac{5\pi}{4}\)

C. \(12-2\pi\)

D. \(12-\pi\)

E. \(6- \frac{\pi}{2}\)

Similar question to practice: two-wheels-are-connected-via-a-conveyor-belt-the-larger-133697.html

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Did not understand any of the solutions above. Bunuel chetan2u please share your approach to this problem. Thanks

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 12 meters long, so the two straight pieces of the belt have a combined measure of (12 - π), which means the distance between the centers of the circles is (12 - π)/2 = 6 - π/2.

Answer: E
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