Author EstellMedema32 in Mathematics, 06.11.2019

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

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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