Question

the cans must have a volume of exactly 1 cubic foot. the material for the top and bottom of each can cost $5 per square foot, while the material for the side of the can cost $4 per square foot. express the cost C (in $) of producing one can as a function of the radius (in feet) of the base.

Answer 1

let the height of the can be h ft

let the radius of its base be r ft
Volume = π r^2 h
1 = πr^2 h
h = 1/(π r^2)

cost = 5(2πr^2) + 4(2πrh)
= 10πr^2 + 8πr(1/πr^2)
= 10π r^2 + 8/r

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