radius and height of cone

Hi I have done these types of problems but I have missed something this time.

Have a circle with radius of 10. I remove a sector with an angle at the radius of 120 degrees. the remains of the circle (looks like pac-man) are joined to make perfect cone (no overlapping).

I need to find the radius of the base of the cone and the vertical height of the cone from the centre to the point.

My thoughts are:

1.calculate the circumference of the circle remains ie. (360-120)*2*pi*10=40pi/3

2. find r for base of cone. 40pi/3=2pi(r)-->40pi/3/2pi=r.

3. side view of cone will be 2 congruent right triangles sharing vertical side with hyp =10.

4. Use pythag to solve for height h^2=10^2-(40pi/3/2pi)^2.

Any thing wrong with my method?

Thanks,

Neverquit