Physics can you help and give the formula!!?

Question

Gold has density of 19.3 103 kg/m3. What would the radius of a solid gold sphere have to be if the acceleration due to gravity at its surface is to be 9.81 m/s2? Check your answer against the radius of the Earth, which has a mean density of 5.5 103 kg/m3.
r = _____km???

Answer 1

M1=M2
V1p1=V2p2
V=4/3piR^3 then

4/3piR1^3 p1 = 4/3piR2^3 p2

finally

R1 =R2 ( p2/p1 )^1/3

R1= R2 (5.5 E+3/19.3 E+3 )^1/3
R1= 0.658 R2

Let the radius of Earth be R2=6,380 km
then
R1=4,200 km