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Math Help - Cost of a Can

  1. #1
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    Cost of a Can

    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 material that costs 6 cents per square centimeter, while the sides are made of material that costs 4 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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  2. #2
    Super Member Matt Westwood's Avatar
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    Let V = the volume of the can.
    Let h = the height of the can.

    We know that the surface area of the top and bottom of the can is 2 times (pi r^2) - it's 2 times because there's two of them.

    The cost of the material is 6 cents per cm^2 so the cost of the top and bottom are 6 x 2 pi r^2 = 12 pi r^2.

    The area of the sides is equal to the perimeter times the height, which is 2 pi r h.

    The cost of the material is 4 cents per cm^2 so the cost of the sides is 4 x 2 pi r h = 8 pi r h.

    We don't know what h is but we do know that V = pi r^2 h, so we can get this in terms of h, that is, h = V / (pi r^2) and then plug that into our equation.

    So the total cost is:

    12 pi r^2 + 8 pi r (V / pi r^2)

    ... and we know what V is, it's 500.

    So the total cost is 12 pi r^2 + 8 x 500 / r

    etc.

    Just needs to be simplified a bit and then get the calculator out.
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  3. #3
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    Good job!

    It's great to have people like those on this website helping students with math.
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