How Do You Calculate the Length of a Belt in a Standardized Test Problem?

[member 508213]

I was taking a test yesterday and this question came up, it could possibly be the only one I missed on the test. I roughly sketched and described the problem to the best of my memory, but I guarantee that all of the essential information is there. I have attached the problem to this question please view it so you can help me out better.

Discussing the problem: Since you need to find the length of the belt, I first found the portion covering the circles and since the circumference of the circles are 10pi and 2 pi respectively, I multiplied by the ratio that the belt covered of the circles, which were 2/3 and 1/3. So when you add those numbers together you get 22pi/3 and then all that is left is to find the length of the belt in between the two circles. This is where I got stuck, I looked at the answer choices and one of them had 22pi/3 + 8, and the other had 22pi/3 + 8(√3). I chose the second option but I have no idea how to actually finish this problem and would appreciate the help, thank you.

 

[jedishrfu]

This image may help:

http://mathcentral.uregina.ca/QQ/database/QQ.09.04/ian2.1.gif

note the right triangle AED do you see how to do it now?

 

[member 508213]

Yes thank you very much! It was difficult to visualize it like that for me during the test but it is very clear how to complete the problem with this picture

 

[member 508213]

Yes thank you very much! It is much easier to visualize with the picture.