Thread: A maximum/minimum problem

Prove that a closed cylinder of fixed surface area has maximum volume when its diameter equals its height

For this question I have two equations,

V = (pi)r^2h
AND
SA = 2(pi)r^2+2(pi)rh which equals a constant, or C

Could someone help me find an equation to find the maximum volume and prove that it would be when diameter equals height?

Thankyou =)

If the SA is constant then when you differentiate it the constant will become zero. Try manipulating the equation after you differentiate it.