1. ## 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

2. 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.

3. 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.