Some things are not possible to explain but using mathematics, so
you are going to have to persevere.
You need to start with metal disk of the area, which when domed
should become of required size. There are few principals involved:
Deformation - when metal is deformed, the outer layer stretches,
and the inner compresses; the middle layer is unchanged. That is why
a pipe is as strong as a rod. Therefore all calculations are done
using middle layer. In you case it is 7.5mm.
Geometry - a dome is 1/2 of a sphere, so calculating area of a
sphere and dividing by 2 would yield the result.
A(surface area of a sphere) = Pi( constant = 3.14 ) * D^2(diameter
of a sphere squared) = A = 3.14 * ( 7.5 * 7.5) = 3.14 * 56.25 =
176.625 = 176.6 mm^2 ( one decimal place is good enough precision )
176.6 / 2 = 88.3 mm^2 which is area of the starting disk.
However, when we work with metal, metal stretches. By how much, will
depend on individual technique. For beginners it may be necessary 20%
correction. As technique improves, the amount of correction
decreases. Using 20%, the area of starting disk becomes 70.6 mm^2.
Area of a disk = Pi*r^2, so r (radius of starting disk) = square
root( A / Pi ) = square root ( 70.6 / 3.14 ) = 4.74 mm So diameter of
starting disk is 4.74 * 2 = 9.5 mm approximately.
Using 10% correction - sqrt((88.3 * 0.9)/3.14)*2 = 10 mm
Since amount of deformation depends on the thickness of the metal (
the same technique will result in more metal stretching depending on
thickness ) a formula incorporating this dependence is useful.
D disk = (D(outside) - thickness of metal) * Pi * (1 - Correction) /2
D disk = ( ( 8 - 0.5 ) * 3.14 * ( 1 - 0.1) ) / 2 = 10. 6 mm
So the range is from 9.5 to 10.6. You would need to experiment to
find out what is your number is. Important to remember individual
technique can significantly influence any formula.