What is the Derivation for Pressure at the Centre of a Star?

[Brewer]

I've been asked to derive the pressure at the centre of a star (well show that it is (Gm^2)/(8*pi*R^4).)

I've worked it through as follows:

Pressure = force/area

f=G*m^2/R^2

surface area = 4*pi*R^2

and then I put the two formulas together but as you can see I only have a 4 on the bottom instead of 8. Have I missed something clearly obvious here?

Any help would be appreciated.
Thanks

 

[Tide]

If you're looking for the pressure at the center of the star why are you using the force and area at the surface of the star?

 

[Brewer]

Because I couldn't think of another way to do it - it seemed logical to me when the equation I had to get has both the radius and mass of the star. Am I totally lost?