I am very sorry, earboth.

**<--- why?**
So now I would have to find the radius of the cone.

I discern that triangle VDO is similar to triangle VCA.

So:

$\displaystyle \dfrac{CA}{3\left(\frac{1}{3}\right)}$ $\displaystyle = \dfrac{12}{8}$ (corr. sides of similar triangles)

CA =

**5cm** **<<<<<<**
Volume of the cone is $\displaystyle \dfrac{1}{3}\pi r^2h$

= $\displaystyle \dfrac{1}{3}\pi5^2(12)$

$\displaystyle = 100\pi$

**<<<<<<**
So the volume of cone that is not occupied by the sphere is:

$\displaystyle 100\pi - \dfrac{4000}{81} \pi$

Am I on the right track?