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Answered by **AL2006**

The volume of a sphere is (4/3) (pi) (radius cubed).The volume of one sphere divided by the volume of another one is (4/3) (pi) (radius-A)³ / (4/3) (pi) (radius-B)³Divide top and bottom by (4/3) (pi) and you have (radius-A)³ / (radius-B)³and that's exactly the same as ( radius-A / radius-B ) cubed.I went through all of that to show you that the ratio of the volumes of two spheresis the cube of the ratio of their radii.Earth radius = 6,371 kmPluto radius = 1,161 kmRatio of their radii = (6,371 km) / (1,161 km)Ratio of their volumes = ( 6,371 / 1,161 ) cubed = about 165.2Note: I don't like the language of the question where it asks "How many spheres...".This seems to be asking how many solid cue balls the size of Pluto could bepacked into a shell the size of the Earth, and that's not a simple solution.The solution I have here is simply the ratio of volumes ... how many Plutos can fit into a hollow Earth if the Plutos are melted and poured into the shell.That's a different question, and a lot easier than dealing with solid cue balls.

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