volume inside a solid solid angle

Question

Is it right to say that in a sphere of radius R, the volume inside a solid angle $\Omega$ is just : $V=\frac{4\pi R^3}{3}\frac{\Omega}{4\pi}=\frac{R^3 \Omega}{3}$ ?

Answer 1

Yes, in another way we can see that the volume of a spherical sector of radius $r$ is $$ V=\frac{rA}{3} $$ where $A$ is the area of the cap that is $A=\Omega r^2$