Consider a right circular cylinder whose total surface area (top, bottom, side) is 300 pi; what must its radius be in order that the volume be as large as possible

Answer 1

2πr^2 + 2πrh = 300
h = (300-2πr^2)/2πr
= 150/πr - r

v = πr^2 h = πr^2(150/πr - r)
= 150r - πr^3

dv/dr = 150-3πr^2
max v occurs when r=√(50/π)