SOLUTION: You want to manufacture soup cans in the shape of a cylinder. Each can will have a volume of 1099 cubic centimeters. You want to choose the dimensions so that the surface area is m
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Question 1026186: You want to manufacture soup cans in the shape of a cylinder. Each can will have a volume of 1099 cubic centimeters. You want to choose the dimensions so that the surface area is minimized. What dimensions should you choose for the cans? Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! You want to manufacture soup cans in the shape of a cylinder. Each can will have a volume of 1099 cubic centimeters. You want to choose the dimensions so that the surface area is minimized. What dimensions should you choose for the cans?
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Vol = pi*r^2*h --> h = Vol/(pi*r^2)
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Area = 2pi*r*h + 2pi*r^2
Sub for h
Area = 2*Vol/r + 2pi*r^2
dA/dr = -2Vol/r^2 + 4pi*r = 0
-2*Vol + 4pi*r^3 = 0
r^3 = 2198/4pi
r =~ 5.592 cm
h = 11.184 cm
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Min area is h = 2r for any cylindrical container
