Question

A closed-topped cylindrical tin can is to be made with a volume of
25 cm ^3.
a) Determine a function to model the height h, of a can in terms of the radius, r.
b) Determine a function to model the surface area A, of the can in terms of the radius, r.
c) What is an appropriate domain for the surface area function, A(r).

Answer 1

pi r^2 h = 25
so
h = 25/(pi r^2)

A = 2 pi r^2 + 2 pi r h
but we know h(r)
A = 2 pi r^2 + 2 pi r * 25/(pi r^2)

A = 2 pi r^2 + 50/r

r better be >0