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) (Show Source): You can put this solution on YOUR website!
We know that, from the constraint, h = 30 - r. Hence, the volume V is
(30 - r) = -\pi r^3 + 30\pi r^2)
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
(10) = 4000\pi)
cm^3.
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