Calculus Word Problem

Jun 2010
3
0
Fairplay, MD
Find the angle of the sector that should be removed from a circular piece of canvas so that the cone formed with the remaining canvas has the largest volume.
 
May 2009
72
21
Brooklyn, NY
Have you derived the equation for the volume of the cone with some constant slantlength s (the radius of your circle), and some variable base b (the circumference of the remaining sector, a function of s and the removed angle t) ? Once derived, you can apply calculus to find its critical point(s) as function(s) of t.
 
Jun 2010
3
0
Fairplay, MD
Almost

There are two variables: The base b of the cone, and the height h of the cone. There must be a way to put b in terms of h. Also, I think the angle of the sector should be measured in radians.
 
Jun 2010
3
0
Fairplay, MD
Solution Found!

Thanks for the help! I was able to come up with a simple but elegant solution to this problem. Again, Thanks!