Confused on C2

A closed cylinder has total surface area equal to 600pi. Show that the volume Vcm^3, of this cylinder is given by the formula V = 300pi r - pi r^3, where r cm is the radius of the cylinder.

(b) Find the maximum volume of such a cylinder

Help is very much appreciated

Reply 1

k@tie

600pi = 2piR^2 + 2piRH = 2piR(R+H)
300 = R(R+H)
R+H = 300/R
H = 300/R - R
Volume = piR^2H = piR^2(300/R - R) = 300piR - piR^3
dV/Dr = 300pi - 3piR^2
0 = 300pi - 3piR^2
100 = R^2 =>R=10