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April 17, 2015

April 17, 2015

Posted by **lisa** on Saturday, March 2, 2013 at 10:17pm.

Find the height in centimeters of the most economical container.

- calculus -
**Reiny**, Saturday, March 2, 2013 at 11:57pmlet the radius be r

let the height be h

V = πr^2 h

πr^2 h = 20π

h = 20/r^2

Cost = .40(2πr^2) + .32(2πrh)

C = .8πr^2 + .64πr(20/r^2)

= .8πr^2 + 12.8π/r

dC/dr = 1.6πr - 12.8π/r^2

= 0 for a min of C

1.6πr = 12.8π/r^2

1.6r^3 = 12.8

r^3 = 8

r = 2

then h = 20/4 = 5

the cylinder should be 5 cm high and have a radius of 2 cm.

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