Key to symbols
P= pressure in Pa
p= mean density = 5.51 x 10 to power of 3 kg per cubic meter
R = radius of planet =6.37 x 10 to the power of 3 km
G = universal gravitation constant = 6.67 x 10-11 N m2 kg-2

Equation for the pressure at the centre of the planet is

P = 2 pi G   p2 R2
    ------
      3

1) Calculate the expected pressure at the center of the planet
(include all workings)

2) Rearrange the equation to the answer in the form R =.....

Tip paid for quick, informative and accurate answer

Hello desperateforhelp, here we go:

P = 2 pi G p^2 R^2 / 3

I verified your formula and values here:
http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/Mathematical_Thinking/grvtysp2.htm

P = 2(3.1416)(6.67 x 10^-11)(5.51 x10^3)^2(6.37 x 10^6)^2 /3
NOTE: I changed 6.37 x 10^3 km to 6.37 x 10^6 m to get rid of the km units

P = 2(3.1416)(6.67 x 10^-11)(30.3601 x 10^6)(40.5769 x 10^12) /3

P = 2(3.1416)(8216.898 x 10^7) /3

P = 17209.471 x 10^7

P = 1.7208 x 10^11 N/m^2

I didn't show units on the above because it would have been very
confusing. Here is how the units work out:

P(N/m^2) = Nm^2/kg^2 x (kg/m^3)^2 x m^2

         = Nm^2 x kg^2 x m^2 / kg^2 x m^6 
The kg^2 in the numerator cancels out the kg^2 in the denominator and
the m^4 in the numerator divided by m^6 in the denominator equals m^2 giving:
         = N / m^2

So the units do check out. Also note that we get the same answer as
was obtained in the link above.

The second part of your question is:

P = 2 pi G p^2 R^2 / 3
Multiplying both sides by 3 we get:

3P = 2 pi G p^2 R^2
Dividing both sides by 2 pi G p^2 we get:

3P / 2 pi G p^2 = R^2
Taking the square root of both sides we get:

(3P / 2 pi G p^2)^-2 = R  

Or:

R = (3P / 2 pi G p^2)^-2 

This should complete your answer. If there is any of this you don't
understand, please ask for a clarification and I will try and explain.

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Request for Answer Clarification by desperateforhelp-ga on 14 Sep 2004 14:48 PDT

Really helpful - thanks redhoss!, one question:

The end of your answer to part one is :

P = 17209.471 x 10^7

P = 1.7208 x 10^11 N/m^2

Should the last line read 1.7209 x ....... instead of the 1.7208 x ..... as shown?

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Clarification of Answer by redhoss-ga on 14 Sep 2004 15:26 PDT

Yes, it should read P = 1.7209 x 10^11 N/m^2 . My typing skills are
not very good. Glad you caught my error.

Thanks for the detailed answer and your clarification redhoss.