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October 16th, 2011, 07:17 PM   #1
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Right Circular Cone

Find the volume V of the described solid S.
A frustum of a right circular cone with height h, lower base radius R, and top radius r




This one I am not sure about. I guess they are just asking for a general formula because they dont give any numbers?

My best guess is to integrate the volume of a cylinder from R to r:



but I think that is reaching at best.
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October 16th, 2011, 07:43 PM   #2
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Re: Right Circular Cone

Think of it as a volume by slicing, where we slice the frustum into a stack of disks:



x will be a linear function of y, passing through the points (R,0) and (r,h):

thus we have:



Let giving:

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October 16th, 2011, 07:58 PM   #3
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Re: Right Circular Cone

Impressive. The solution is so much more involved that I expected.
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October 19th, 2011, 12:10 AM   #4
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Quote:
Originally Posted by aaron-math
Find the volume V of the described solid S.
Can the standard formula base area height/3 for the volume of a cone be used? It would make this problem easy.
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