Posted by **Luke** on Monday, November 23, 2009 at 1:30am.

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?

For my answer I got:

radius: 49.6117

height (in this case length): 58.1962

Could someone confirm my answers? Thank you very much.

- Math, not "Chandra" -
**Writeacher**, Monday, November 23, 2009 at 9:45am
Assistance needed.

Please type your __subject__ in the **School Subject** box. Any other words are likely to delay responses from a teacher who knows that subject well.

- Chandra -
**drwls**, Monday, November 23, 2009 at 10:41am
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.

If that is what you did, and no mistakes were made, than your answers are correct

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