The largest solid angle subtended at the center of a hemisphere of diameter will be
The largest solid angle subtended at the center of a hemisphere of diameter will be 4π.
his result can be derived from the formula you mentioned:
ω = A/r2
A is the area of the surface and r is the distance from the point to the surface.
In the case of a sphere, the area A is equal to 4πR2
R is the radius of the sphere.
Therefore, the solid angle subtended by the sphere at its center is:
ω = (4πR2) / R2 = 4π steradians
This result is independent of the size of the sphere, as long as it is a perfect sphere.