SOLUTION: an aluminum can us being designed to hold 17013pi cubic centimeters of water. Find the dimensions of the can that result in the lest amount of aluminum used in the construction of

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Question 672605: an aluminum can us being designed to hold 17013pi cubic centimeters of water. Find the dimensions of the can that result in the lest amount of aluminum used in the construction of the can
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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an aluminum can us being designed to hold 17013pi cubic centimeters of water.
Find the dimensions of the can that result in the lest amount of aluminum used
in the construction of the can
:
Volume
pi%2Ar%5E2%2Ah = 17013%2Api
divide both sides by pi
r%5E2%2Ah = 17013
divide both sides by r^2
h = 17013%2Fr%5E2
:
Surface area of a cylinder; (including the ends)
S.A. = 2%2Api%2Ar%28r+%2B+h%29
:
Replace h with 17013%2Fr%5E2
S.A = 2%2Api%2Ar%28r%2B%2817013%2Fr%5E2%29%29 = 2%2Api%2A%28r%5E2%2Br%2817013%2Fr%5E2%29%29 = 2%2Api%2A%28r%5E2%2B%2817013%2Fr%29%29
Graphically

Can radius for minimum surface area = 20.41 inches
:
Find the height of the cann
h = 17013%2F20.41%5E2
h = 40.84 cm high
:
:
:
Check by finding the vol of a can with a radius of 20.41 and a height of 40.84
Vol = pi%2A20.41%5E2%2A40.84
V = 53447 cu/in; (which is 17013%2Api%29)