Maximum volume based on radius.

Question

The surface area of a cylinder is 200 units squared. Find the radius so that the volume is maximized.

Answer 1

Since this problem is given in a precalculus course, I will not use Calculus to solve it.

The volume of the cylinder = pi x r^2 x h = 200

-------  h = 200/(pi x r^2)

 

Surface area = 2 x pi x r^2 + 2 x pi x r x h

                    = 2 x pi x r^2 + 400/r

 

Use a graphing utility to graph

y =  (2 pi) x^2 + 400/x

From your graph, locate the value of x at which y is a mximum.

x  = 3.2 units