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2 November, 12:46

A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of a material that costs 11 cents per square centimeter, while the sides are made of a material that costs 8 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder.

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  1. 2 November, 12:58
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    The answer to the question is

    The total cost C of the material as a function of the radius r of the cylinder is

    0.6912·r² + 800/r Dollars.

    Step-by-step explanation:

    To solve the question, we note that

    The area of the top and bottom combined = 2·π·r²

    The area of the sides = 2·π·r·h

    and the volume = πr²h = 500 cm²

    Therefore height = 500 / (πr²)

    Substituting the value of h into the area of the side we have

    Area of the side = 2πr·500 / (πr²) = 1000/r

    Therefore total area of can = Area of top + Area of bottom + Area of side

    Whereby the cost of the can = 0.11*Area of top + 0.11*Area of bottom + 0.8*Area of side

    Which is equal to

    0.11*2*π*r² + 0.8*1000/r = 0.6912·r² + 800/r

    The cost of the can is $ (0.6912·r² + 800/r)
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