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Math Help - Problems involving equal surface area and volume

  1. #1
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    Problems involving equal surface area and volume

    I have had a few of these questions (both volume and surface area) and not comfortable with changing the formula over. Any help is appreciated to logical steps for this and other such problems

    Question1
    A cone has radius
    r and slant height l.
    A cylinder has radius
    r and height r.

    The
    total surface area of the cone is equal to the total surface area of the cylinder.

    Find an expression for
    l in terms of r.
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  2. #2
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    Quote Originally Posted by 200001 View Post
    I have had a few of these questions (both volume and surface area) and not comfortable with changing the formula over. Any help is appreciated to logical steps for this and other such problems

    Question1
    A cone has radius
    r and slant height l.
    A cylinder has radius
    r and height r.

    The
    total surface area of the cone is equal to the total surface area of the cylinder.

    Find an expression for
    l in terms of r.
    1. The total surface area of a cylinder is:

    a_{cyl} = 2 \pi r^2 + 2\pi r h

    With h = r you get a_{cyl} = 4\pi r^2

    2. The total surface area of a cone is:

    a_{cone} = \pi r^2 + \pi r l

    3. Both areas are equal:

    \pi r^2 + \pi r l = 4 \pi r^2~\implies~\boxed{l = 3r}
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  3. #3
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    Thanks for your help

    I am still struggling to make the connection between this part:

    With h = r you get

    and this part



    I am trying to work out how you got to those findings

    Regards
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  4. #4
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    Talking

    If you plug "r" in for "h" (because h = r) in a_{cyl}\, =\, 2\pi r^2\, +\, 2\pi rh, what do you get? (Plug "r" in for "h" in the formula you were given, simplify, and note the result.)

    If you solve \pi r^2 l\, +\, \pi rl\, =\, 4\pi r^2 for l\, =, what do you get? (Divide through by \pi r and then solve the resulting literal equation.)

    If you get stuck, please reply showing how far you have gotten. Thank you!
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  5. #5
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    Great, Thanks
    I understand now
    Regards
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