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As shown in the figure above, a thin conveyor belt 12 meters

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As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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

[Reveal] Spoiler:
Attachment:
Convey_Belt.png
Convey_Belt.png [ 6.3 KiB | Viewed 5386 times ]
[Reveal] Spoiler: OA

Originally posted by Dhairya275 on 24 Sep 2013, 13:37.
Last edited by Bunuel on 04 Apr 2018, 09:53, edited 3 times in total.
Edited the question.
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Re: As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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New post 25 Sep 2013, 06:00
Dhairya275 wrote:
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 feet, between the centers of
the two wheels?

A. 2pi
B. (5pi)/4
C. 12-(2pi)
D. 12-pi
E. 6- (pi)/2

Help Please !!


The total length of the conveyor belt = 2*AB+arc(AC+BD) = \(2*AB+2*\pi*r = 12\)

Thus, AB = \(\frac{12-2\pi*\frac{1}{2}}{2} = 6-\frac{\pi}{2}\)

E
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Re: As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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New post 25 Sep 2013, 08:41
Expert's post
Dhairya275 wrote:
Attachment:
Convey_Belt.png
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 feet, between the centers of the two wheels?

A. 2pi
B. (5pi)/4
C. 12-(2pi)
D. 12-pi
E. 6- (pi)/2


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

Hope it helps.
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Re: As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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New post 25 Sep 2013, 10:10
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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Re: As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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New post 04 Apr 2018, 06:27
Did not understand any of the solutions above. Bunuel chetan2u please share your approach to this problem. Thanks
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Re: As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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New post 04 Apr 2018, 09:57
Expert's post
sadikabid27 wrote:
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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Re: As shown in the figure above, a thin conveyor belt 12 meters [#permalink]

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New post 06 Apr 2018, 08:44
Expert's post
Dhairya275 wrote:
Image
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. \(6- \frac{\pi}{2}\)

[Reveal] Spoiler:
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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Re: As shown in the figure above, a thin conveyor belt 12 meters   [#permalink] 06 Apr 2018, 08:44
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