[Math] Point lies inside of the sphere

Question

Let $a,\alpha,\beta$ be any real numbers with $a>0$. Can someone show and explain why the point say $(x,y,z)=(a\sin{\alpha}\cos{\beta},a\sin{\alpha}\sin{\beta},\sqrt{3}a\sin{\alpha})$ lies inside, or on, the sphere with a radius of $2a$ which is centered at the origin.

Answer 1

The equation of such this sphere is $x^2+y^2+z^2=(2a)^2=4a^2$. Now set $$x=a\sin\alpha\cos\beta, y=a\sin\alpha\sin\beta, z=\sqrt{3}~a\sin\alpha$$ in the equation and check if $x^2+y^2+z^2\le4a^2$