Posted by **Anonymous** on Monday, December 15, 2008 at 8:07pm.

A right circular cylinder is inscribed in a cone with height h and base radius r. Find the

largest possible surface area of such a cylinder.

- Calculus -
**Reiny**, Monday, December 15, 2008 at 8:56pm
the the radius of the cylinder by x and the height of the cylinder be y.

(the h and r will be constants)

by ratios : x/(h-y) = r/h

y = (hr - hx)/r

I will assume that you want both top and bottom of the cylinder included in your surface area, if not you will have to change the equation.

SA = 2πx^2 +2πxy

= 2πx^2 + 2πhx - (2πh/r)x^2 after subbing in the above y

SA' = 4πx + 2πh - (4πh/r)x

= 0 for a max/min of SA

I get x = hr/(2h-2r)

put that back into SA = ....

I will let you finish the algebra.

(Also check my steps, I tend to make typing errors)

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