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 $\displaystyle A$ to $\displaystyle B.$

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