# Calculus

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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?

Height?

• Calculus -

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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