Posted by Z32 on Monday, June 22, 2009 at 12:58am.
A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2. What are the dimensions of such a cylinder which has maximum volume?
Radius?
Height?

Calculus  Reiny, Monday, June 22, 2009 at 9:01am
did you make a sketch??
let the radius of the cylinder be r
let the height of the cylinder by h
by similarity I can set up the ratio h/(2r) = 8/2
> h = 84r
volume of cylinder
= pi(r^2)(84r)
= 8pi(r^2)  4pi(r^3)
differentiate, set equal to zero, solve for r, etc
(I got r = 4/3)
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