Question

Calculate the solid angle subtended by an octant of a sphere at the centre of the sphere.

• A. $\frac{\pi }{2}\text{steradian}$
• B. $\frac{\pi }{4}\text{steradian}$
• C. $\frac{\pi }{6}\text{steradian}$
• D. $\pi \text{steradian}$

Answer 1

The correct option is A $\frac{\pi }{2}\text{steradian}$

An octant of sphere is each part of sphere divided by a $3$-axis cartesian system plane.

Its surface area is $S=\frac{1}{8}\times 4\pi r^2=\frac{\pi r^2}{2}$

Solid angle is given by $\Omega =\frac{S}{r^2}$​

$\Omega =\frac{\pi }{2}\text{steradian}$