Spheres & saucers

[David Gaskill]

I am not a mathematician and I was up till the early hours of this
morning trying to solve the problem of building a sphere from circular
panels which are sections of a sphere. I did not succeed and am
appealing for help.

My raw-material is circular slices of a sphere . I don't know what the
mathematical term for these is but they are essentially saucers
created by the taking a slice off a sphere.

If the diameter of the sphere is 100 then the diameter out of my
saucers is 50; the radius of curvature of the saucers is of course 50.
>From each saucer I will cut a rectangular panel and I then wish to
glue these panels together to create my sphere

There is an additional complicating factor - I don't actually wish to
create a complete sphere but a sphere with a slice taken off it. If I
stand this mutilated sphere on a flat surface with the open end
downwards the height of the assembly is to be 90.

I wish to use the minimum number of panels with the minimum number of
different panels sizes and of course I also need to determine what
these panels sizes should be. I am hoping that it will be possible to
do it with two or three different panels sizes.

I am hoping that my description of the problem is sufficiently
comprehensible to allow some kind soul to take pity on me and tell me
what to do.

David