a right circular cone is to have a volume of 120 cubic feet. find the dimensions so that the lateral surface area is as small as possible

Question

a right circular cone is to have a volume of 120 cubic feet.  find the dimensions so that the lateral surface area is as small as possible

valpey · Answer

Are you familiar with the equations for volume of a cone and lateral surface area of a cone?

valpey · Answer

When I think of it, I imagine a paper cone which I slit down one side and turn it into a great arc swept out of a circle.

valpey · Answer

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valpey · Answer

Lateral Surface Area (LSA) will be a function of radius and height, but you can solve for one in terms of the other using the Volume limitation. Once you have LSA in terms of just one variable, you can take the derivative of that expression to find a local minimum for LSA.

anonymous · Answer

can you give me the solution to the given problem sir?

anonymous · Answer

thank you valpey