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Math Help - Surface area of cylinders

  1. #1
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    Surface area of cylinders

    Hi

    This may seem like a very simple problem.

    If you are given the surface area of a sphere how do you find the radius and height. For example if the surface area of a cylinder including both ends in 60^2 how would you find the height and radius.

    Any help would be appreciated
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  2. #2
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    Quote Originally Posted by nikki1234 View Post
    Hi

    This may seem like a very simple problem.

    If you are given the surface area of a sphere how do you find the radius and height. For example if the surface area of a cylinder including both ends in 60^2 how would you find the height and radius.

    Any help would be appreciated
    You say sphere once and cylinder twice so I will guess you mean cylinder.

    The area of the top and bottom are \pi r^2+\pi r^2=2\pi r^2

    And the area of the side is 2 \pi r h

    So the total surface area is

    2 \pi r^2 +2 \pi r h =60 \iff \pi r^2 + \pi r h=30

    Without more information this problem has an infinite number of solutions
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  3. #3
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    Hi

    Its actually a differentiation problem

    the question states if the area of a cylinder including both ends is 60 cm what is the largest possible volume?

    Hope that helps in helping me!
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    Quote Originally Posted by nikki1234 View Post
    Hi

    Its actually a differentiation problem

    the question states if the area of a cylinder including both ends is 60 cm what is the largest possible volume?

    Hope that helps in helping me!
    Well you know the volume of a cylinder is

    V=\pi r^2 h

    and from above you can solve for h to get

    h =\frac{30-\pi r^2}{\pi r}

    If you put this into the volume formula you get

    V=\pi r^2\left( \frac{30-\pi r^2}{\pi r}\right)=-\pi r^3+30r

    Now you need to maximize the volume.

    Since this is a cubic if you want an analytic solution you will need to use calculus and the derivative. If you do not know calculus plot the function on a graphing device and find the maximum volume.
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  5. #5
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    Thank you that was a great help
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