Thread: 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

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 to

Then its length is the circumference of the circle.

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