Question

The solid angle subtended by the total surface area of a sphere at the centre is :

• A. $4\pi$
• B. $2\pi$
• C. $\pi$
• D. $3\pi$

Answer 1

Answer: (A)

$4\pi$

A steradian is the solid angle subtended at the center of a sphere of radius r by a section of its surface area of magnitude equal to $r^2$. Since the surface area is $4\pi r^2$, there are $4\pi$ steradians surrounding a point in space.