A solid ball of radius R has charge density rho has given by rho=rho not (1-r/R).the electric field outside the ball is
From Gauss's law, Electric field outside the ball will not depend on the internal charge distribution it will depend only on the Total charge, so using integration we would first calculate the total charge of the solid ball
the total charge of the solid ball= 2 π ρ(not)R^3
therefore electric field outside the solid ball will be similar to the electric field generated by a point charge of magnitude 2 π ρ(not)R^3