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@Greenbank
The long length (of each piece) is simply a right angle triangle with sides R and H.
L = sqrt( R2 + H2)
For the length B think of the top down view, you have an isoceles triangle with an internal angle 45o and two sides of length R.
You can split this up into two right angled triangles with hypoteneuse length R and opposite angle 22.5o.
sin 22.5 = opp / hyp
opp = R * sin 22.5
So half B would be 0.38268 (5dp) * R
So B would be 0.76537 (5dp) * R