I have a semi-project due tommorrow that basically asks the following question: If you are designing a tent in the shape of a spherical cap (a sphere with the lower portion sliced away by a plane) and the material used for the roof costs 2.5 times more per(adsbygoogle = window.adsbygoogle || []).push({}); squarefoot than the material used for the floor, what should the dimensions of the tent be to minimize the cost of materials used? Additional info: the volume of the tent will be 150 cu ft.

Goal: To derive a formula for maximum cost efficiency while retaining the original volume and shape of the tent.

The most difficult part of this problem is simply knowing where to start. I realize that when optimizing, I have to keep the minimums and maximum values of my equation in mind. In this case, I want to use as little ceiling material as possible for the tent while making sure that it remains a dome-shaped tent. Formulas used in this problem are the "volume of a dome" equation which I believe is V=((pi*h)/6)(3r^2+h^2) and the surface area formula of a dome: S=pi(h^2+r^2).

I wish I knew where to go from this beginning point, because short of taking the derivatives of these functions (with respect to what though?), I don't know to do.

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# Homework Help: Spherical Optimization and beyond

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