How much would density be of each planet have to change to have same volume as Earth?

Question

Research the solar system to find the mass and diameter of each planet. Assume each planet is a perfect sphere and calculate the density of each planet using the formula: density= mass/volume. By how much would the density of each planet have to change if each planet increased in size or decrease in size so that it had the volume as the Earth?

~~ From book College Geometry A Problem- Solving Approach 2nd Edition Section 3.5 problem 56.

Answer 1

The general form for density D=M/V. Applying this formula to the Earth, DE=ME/VE. So, if V is the volume of a planet, V/VE is the proportion of its volume in relation to Earth. If the planet is bigger than Earth, then V/VE>1 and compressing its mass into the same volume as the Earth would increase its density by the same factor. So the density would change to D.V/VE. There would be a decrease in density if V<VE. But D=M/V, so the change in density would simply be M/VE. This is of course the mass of the planet squeezed or expanded into Eath's volume.

The density of water is 1g/cc=1E12kg/km^3. The density of the planets is best shown using the density of water as the unit. Treating every planet as a perfect sphere and knowing the mean radius of each we can work out the volume and calculate the density.

PLANET	Radius (km)	Mass (kg)	Volume (km^3)	Density (compared to water)	Changed density
Mercury	2440	3.30E23	6.09E10	5.42	0.30
Venus	6052	4.87E24	9.29E11	5.25	4.48
EARTH	6378	5.97E24	1.09E12	5.49	5.49
Mars	3397	6.42E23	1.64E11	3.91	0.59
Jupiter	71492	1.90E27	1.53E15	1.24	1748
Saturn	60268	5.68E26	9.17E14	0.62	523
Uranus	25559	8.68E25	6.99E13	1.24	80
Neptune	24766	1.02E26	6.36E13	1.60	94
Pluto	1150	1.27E22	6.37E9	1.99	1.17