find the radius and height of a cylindrical soda can with a volume of 21in^3 that minimize the surface area.

Answer 1

radius -- r
height --- h
given: πr^2 h = 21
h = 21/(πr^2)

Surface area (SA) = 2πr^2 + 2πrh
= 2πr^2 + 2πr(21/(πr^2)
= 2πr^2 + 42/r
d(SA)/dr = 4πr - 42/r^2
= 0 for a max/min of SA
4πr = 42/r^2
r^3 = 42/(4π)
r = (42/(4π)^(1/3) = 1.495163.. or appr 1.5
then h = 21/(πr^2) = 2.99027 or appr 3

notice the h = 2r