# math

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A container in the shape of a right circular cylinder with no top has surface area 3*pi (m2). What height h and base radius r will maximize the volume of the cylinder ?

• math -

surface area = πr^2 + 2πrh = 3π
r^2 + 2rh = 3
h = (3 - r^2)/(2r)

V = πr^2h = (πr/2)(3-r^2)
= (3π/2)r - (π/2)r^3

dV/dr = 3π/2 - (3/2)πr^2
= 0 for a max/min of V
(3π/2)r^2 = 3π/2
r^2 = 1
r = ± 1, but r > 0
r = 1

then h = (3-1)/2 = 1

check my arithmetic

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