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/(2-r) = 8/2

---> h = 8-4r

volume of cylinder

= pi(r^2)(8-4r)

= 8pi(r^2) - 4pi(r^3)

differentiate, set equal to zero, solve for r, etc

(I got r = 4/3)

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