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Geometry cylinder problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by chetan.sharma » Mon Apr 25, 2016 4:58 am
Emeka N. wrote:How should I be thinking about problems like this one?
Hi,
we can see that the belt covers half the circumference of left wheel and half the circumference of right belt..
so it overall covers the entire circumference, which is 1*pi..
so the rest of the belt =15-pi..
this belt covers two times the distance between the centre of the wheels..
so our answer = (15-pi)/2
A
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by ceilidh.erickson » Mon Apr 25, 2016 8:45 am
Here's an image to help clarify Chetan's point:

Image

The distance between the two centers is the same as the distance from the top of one circle to the top of the other. In other words, half of the non-circular part of the belt.

We can think of the belt as 2 curves (half-circles) + 2 straight lines:

Image

The two half-circles together would have the same circumference as a full circle: 1Ï€

Thus, the two straight lines would be the total of 15 minus the two half circles: 15 - π

One of those straight lines would thus be (15 - π)/2
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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