FWIW, i think their description for the radiation shielding is fine. Your analysis is off. If we assume the spherical case, the mass of the shielding is proportional to surface area, not the volume[0]. You might be confusing general radiation shielding and thermal shielding. Thermal shielding is easier because you can point things towards the sun, earth, and moon.
I am more concerned about heat dissipation, which should scale with surface area, but heat generation scales with compute volume.
[0]:
shell thickness, t
compute radius, r
shell volume is (r+t)^3 - r^3 = 3 r^2 t + 3 r t^2 + t^3 = O(r^2)
shielding/compute is O(r^2)/O(r^3) = O(1/r), ie their linear decrease
I am more concerned about heat dissipation, which should scale with surface area, but heat generation scales with compute volume.
[0]:
shell thickness, t
compute radius, r
shell volume is (r+t)^3 - r^3 = 3 r^2 t + 3 r t^2 + t^3 = O(r^2)
shielding/compute is O(r^2)/O(r^3) = O(1/r), ie their linear decrease