A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.

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- Jan 27th 2008, 07:02 AMdoctorgkOptimization
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 12 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area.

Thank You - Jan 27th 2008, 08:32 AMHenderson
Since [tex]V = \frac {4}{3} \pi r^3 + \pi r^2 h[/tex],

[tex]12 = \frac {4}{3} \pi r^3 + \pi r^2 h[/tex] and

Also, , which is

.

Simplify, derive, set equal to zero, and solve.