Fit multiple peices of B inside of Peice A

Hello all,
Im in the process of building an icecream stand for a client.
They want a 47" diameter arch - 9' long for the top.
My plan is to cut out 47" x 3" wide diameter ribs (arches) then support them
in the middle then put bendy ply over it.
Im figuring 6 arches for support - id like to be able to cut them all out on
1 sheet of ply.
Does anyone know how to automagically layout a peice w/in another peice?
Ie - I draw a 4'x8' box.- Part A (the plywood)
I then draw the arch - 47" OD, 43" ID - Part B (the arch)
then have it fit as many of Part B inside Part A?
Doing it by hand right now - I can fit 5.
2 on the top
2 on the bottom (layed out like the Macdonalds arches on top of each other)
then 1 more in the middle facing like a U
Id like to somehow fit 6 on 1 sheet.
Any help would be great.
Thanks
-Rob