SOLUTION: A right-circular cylinder has a radius r cm and a height h cm. Given that h + r = 30, find the maximum volume of the cylinder.

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Question 445838: A right-circular cylinder has a radius r cm and a height h cm. Given that h + r = 30, find the maximum volume of the cylinder.

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We know that, from the constraint, h = 30 - r. Hence, the volume V is

If we suppose V is a function of r, we can take the derivative of V with respect to r:



The derivative is zero when r = 0 or r = 20. Clearly, r = 0 would imply V = 0. It can be checked that r = 20, h = 10 maximizes the volume, which is

cm^3.