Optimization Problems

Question

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 6 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to three decimal places.)

Answer 1

πr² + πr²h = 6

h = (6 - πr²) / πr²

S(r) = 2πr[(6 - πr²) / πr²] + 4πr

Can you determine S'(r), set equal to zero, and answer?

Answer 2

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