Water flowing into hemisphere rates

Water is flowing into a hemispherical container of radius 10cm at a constant rate of 6cm³ per second. It is known that the forumla for the volume of a solid segment cut off a sphere is

$\displaystyle

V = \frac{\pi}{3}h^2(3r - h)

$

where r is the radius of the sphere and h is the height of the segment.

a. Find the rate at which the height of the water is rising when the water height is 2cm.

b. Find the radius of the cirucular water surface when the height is h, and hence find the rate of increase of the surface area when the water height is 2cm.

I have managed to get through part a with no problem, but am totally stuck on part b. The book claims that

$\displaystyle

r= \sqrt{2hr - h^2}

$

and

$\displaystyle

\frac{8}{3}cm^2/s

$

I tried doing it using similar triangles and got nothing at all like that

thanks

jacs