posted by Z32 .
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?
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
= 8pi(r^2) - 4pi(r^3)
differentiate, set equal to zero, solve for r, etc
(I got r = 4/3)