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that solution is wrong. it should be to minimise the cost function and not the surface area of the pool. the cost function is 2*pi*(r^2) plus 2*pi*r*h which is then multiplied by price per square unit of the wood (which is a constant so does not effect the solution)

Since the ceramic costs twice as much as the wood, that must be factored into the cost equation, which will look like this (x=radius):

2*pi*x^2+10/x

The rest of the steps in the solution are correct, so the answer will be X, or the radius, equals (5/2pi)^1/3

Calculus

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