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).
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).
Answers
Damon
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
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