The largest solid angle subtended at the center of a hemisphere of diameter will be

Question

RRB Paper · Accepted Answer

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

where

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

where

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.

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