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Math Help - How to calculate length of a radial line?

  1. #1
    Newbie momi's Avatar
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    How to calculate length of a radial line?

    I have to design a fruit bowl.Its surface will be lacquered with a very expensive lacquer, several radial lines will be inlaid with gold leaf, and the material for the bowl will be an expensive alloy.I have to include in my design a calculation of the volume of the bowl, its surface area and the length of a radial line (either on the interior or the exterior of the bowl).
    My bowl will be a hemisphere. I have found the surface area and volume.
    How can I find the length of the radial line?

    Thanks
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  2. #2
    Super Member

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    Hello, momi!

    I have to design a hemispherical fruit bowl.
    Its surface will be lacquered with a very expensive lacquer,
    several radial lines will be inlaid with gold leaf,
    and the material for the bowl will be an expensive alloy.

    I have to include in my design a calculation of the volume of the bowl, its surface area
    and the length of a radial line (either on the interior or the exterior of the bowl).
    I have found the surface area and volume.
    How can I find the length of the radial line?
    Code:
               r         r
          * - - - - * - - - - * B
          *         :         *
                    :
           *        :r       *
            *       :       *
              *     :     *
                  * * *
                    A

    If I understand it correctly, the radial line runs from A to B.

    Then its length is \tfrac{1}{4} the circumference of the circle.

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  3. #3
    MHF Contributor

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    If the sphere has radius r, then the radial line will have length \pi r. That is half the circumference of the circle the radial line is following, as Soroban says.
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