Question

A hollow cylinder, open at one end, is constructed of thin sheet metal. The total external surface area of the cylinder is 192pi cm^2. The cylinder has a radius of r cm and a height of h cm.
(i) express h in terms of r and show that the volume, Vcm^3 of the cylinder is given by
V=pi/2(192r-r^3).

Answer 1

S A = r² π + 2 r π h
192 π = r² π + 2 r π h   / : π
192 = r² + 2 r h
2 r h = 192 - r²
h = (192 - r² ) / 2 r 
V = r² π h = r² π ( (192 - r² ) / 2 r ) =
= π / 2 ( 192 r - r³ )