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December 20, 2014

December 20, 2014

Posted by **Joey** on Wednesday, March 24, 2010 at 5:06pm.

- Calculus (optimization problem) -
**Damon**, Wednesday, March 24, 2010 at 5:39pmVolume = V = pi r^2 h = constant

so pi r^2 = V/h

and r =(V/[pi h])^.5

and

cost = 5 pi r^2 + 2 pi r h

cost = 5 V/h + 2 pi r h

cost = 5 V/h + 2 pi (V/pi)^.5 h^.5

d cost/dh = -5 V/h^2 + 2 pi (V/pi)^.5 (.5)(h^-.5)

0 when

5 V/h^2 = pi^.5 V^.5 h^-.5

h^1.5 = 5 V^.5/pi^.5

h^3 = 25 V/pi

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