We discover an exoplanet, Planet X, which has the following
   measurements:

            (based on transits)   radius R  =  9 +/- 2  x 10<sup>6</sup> m

     (based on radial velocity)   mass   M  =  6.0 +/- 0.5 x 10<sup>24</sup> kg


       Q:  What is the range of densities consistent with these values?

               The middle of the range is

                               6.0  x 10^(24) kg
             rho(middle)  =  -------------------------------  =  2000 kg/m^3
                              (4 pi/3)  [ 9 x 10^6 m ]^3



               The minimum value consistent with the measurements is

                               5.5  x 10^(24) kg
             rho(min)     =  -------------------------------  =   990 kg/m^3
                              (4 pi/3)  [ 11 x 10^6 m ]^3


               The maximum value consistent with the measurements is

                               6.5  x 10^(24) kg
             rho(max)     =  -------------------------------  =   4500 kg/m^3
                              (4 pi/3)  [  7 x 10^6 m ]^3



           So the full range of density is   990 - 4500  kg/m^3.



       Q:  Is the planet  water/ice  or  rocky?


             Given this range, compositions of both 100% water or 100% rock
             are quite possible.  We really don't know what this planet's
             surface would be like.