# Calculus

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Find the maximum volume of a cylindrical tin that has a total surface area of 600pi cm^2.

• Calculus -

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

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