Pre calculus 12 grade

Question

A right circular cylinder with height h and base raduis r has a total surface area of 90 pi square inches .

Express the volume of the cylinder as a function of r

Answer 1

Area, A= 2πrh+2πr² = 90

h = (90-2πr²)/(2πr) = (45-πr²)/(πr)

Volume, V= πr²h

V(r) = πr²(45-πr²)/(πr) = r(45r-πr²) = 45r-πr³