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November 16th, 2008, 05:01 PM  #1 
Newbie Joined: Nov 2008 Posts: 3 Thanks: 0  maximum volume calculation, please help
Here is the problem, I've been trying to solve but I haven't been able to, please help me! thanks A right circular cone has a height of 10 and a radius of 3. find the dimensions of the cylinder with maximum volume that can fit inside this cone such that the base of the cylinder lies on the base of the cone. Also give maximum volume and verify that the volume is a maximum. 
November 16th, 2008, 07:08 PM  #2 
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: maximum volume calculation, please help
Draw a diagram with a cylinder in the cone. Call the height "h" and the radius "r". Look for similar triangles [a side view will show right triangles] so that you can find r in terms of h or the other way around. Express the volume of the cylinder in terms of r and h [a well known formula by now...or should be.] Then replace r or h by the other so that you have the volume in terms of only one variable. Differentiate and carry on as usual to find max/min.

November 16th, 2008, 08:43 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,814 Thanks: 1046 Math Focus: Elementary mathematics and beyond  Re: maximum volume calculation, please help
See example 2: http://www.cliffsnotes.com/WileyCDA/...eId39895.html 

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