Calculus
posted by Sarah on .
Find the maximum volume of a cylindrical tin that has a total surface area of 600pi cm^2.

a = 2pi r^2 + 2pi rh = 600pi
h = (600pi  2pi r^2)/(2pi*r)
= 300/r  r
v = pi r^2 h
= pi r^2 (300/r  r)
= 300pi r  pi r^3
dv/dr = 300pi  3pi r^2
dv/dr = 0 when r = 10
so, h = 20
max v = pi * 100 * 20 = 200pi