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

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