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Math Help - Cubic Function of a Cylinder

  1. #1
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    Question Cubic Function of a Cylinder

    A rectangular piece of sheet metal with perimeter 50cm is rolled into a cylinder with open ends.

    a) Express the volume of the cylinder as a function of x. Then give the domain of the function.
    b) Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.
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  2. #2
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    Quote Originally Posted by fizz View Post
    A rectangular piece of sheet metal with perimeter 50cm is rolled into a cylinder with open ends.

    a) Express the volume of the cylinder as a function of x. Then give the domain of the function.
    b) Find the approximate value of x that maximizes the volume. Then give the approximate maximum volume.
    what is x supposed to represent?
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  3. #3
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    The circumference of the cylinder. Sorry, I forgot to include that.
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  4. #4
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    side of the rectangular sheet that forms the circumference, C = x

    adjacent side that forms the height of the cylinder, h = 25-x

    x = 2\pi r

    r = \frac{x}{2\pi}


    substitute in the expressions for r and h in terms of x into the cylinder volume formula, then maximize.
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