The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of Pluto does it take to have the same volume as Earth?

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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)³ Divide top and bottom by (4/3) (pi) and you have     (radius-A)³ / (radius-B)³ and 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 spheres is the cube of the ratio of their radii. Earth radius = 6,371 km Pluto radius = 1,161 km Ratio of their radii = (6,371 km) / (1,161 km) Ratio of their volumes =  ( 6,371 / 1,161 ) cubed = about 165.2 Note:  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 be packed 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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