# Chandra

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A building is the shape of an airplane hanger (a half cylinder). Construction for the foundation (rectangular part) costs \$30 per square foot, the sides (semicircle bases) cost \$20 per square foot and the roofing cost \$15 per square foot. The volume of the entire building is 225,000 cubic feet. What should the dimensions of the building be to minimize the cost?

height (in this case length): 58.1962

Could someone confirm my answers? Thank you very much.

• Math, not "Chandra" -

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• Chandra -

How did you get those answers?

For a fixed volume, radius is a function of length.

(1/2) pi r^2 L = 225,000
L (r) = 450,000/(pi r^2)

Cost = L*2r*30 + pi*r^2*20 + pi*r*L*15
Write cost as a function of one variable and set the derivative equal to zero. Then solve for the unknown dimension.

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