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Dhairya275
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same as deadmau5 only that i thought of the problem as
Circumference = 2pi*r so half of the circum of each circle is 0.5pi

0.5pi + 0.5pi = pi
belt = 12
So AB = 12 - pi
Now this length is double (one upside and one downside). So divide by 2. (12-pi)/2 = 6 - pi/2
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Did not understand any of the solutions above. Bunuel chetan2u please share your approach to this problem. Thanks
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Did not understand any of the solutions above. Bunuel chetan2u please share your approach to this problem. Thanks

My approach would not be much different from this one: https://gmatclub.com/forum/as-shown-in- ... l#p1270891 So, could you please tell me what is unclear there?
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Dhairya275

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

Attachment:
Convey_Belt.png

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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