Ellipsoid (lights) explained???

[wingman]

For those interested in getting the most out of their ellipsoid lights:( http://en.wikipedia.org/wiki/Ellipsoid

[Zeuk in Oz]

For those interested in getting the most out of their ellipsoid lights:( http://en.wikipedia.org/wiki/Ellipsoid

Fascinating, however one thing puzzles me :

If the volume of a sphere is : 4/3 Pi rxrxr

Why is the volume of the ellipsoid 4/3 Pi axbxc where a,b & c are the lengths of the 3 semi-axes.

I would have thought it would have been 4/6 Pi axbxc where a,b & c are the length of the axes.

In other words where a=b=c it is called a sphere.

I have never heard of a semi axis.

Is a semi axis half the length of an axis ?

All you mathematicians, help me out here !