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4/3rds pi r cubed.

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Earlier this week I managed to prove to myself, yet again, that I’m not the World’s greatest mathematician.  For the last four years I’ve worked with school children at an event we attend to model our Solar System as if the Sun was a tennis ball.  The problem is that, although the orbits are manageable, the inner planets end up around the size of grains of sand. This year I decided to up my game by using a giant 440mm orange beach ball for the Sun.  Most inner planets could be found within a slice of all-seed bread, and the Gas Giants came out very close to a tomato, a golf ball, and two hazel nuts.  I decided to make Uranus and Neptune at around 14mm diameter from modelling clay, but I grabbed too much clay andNeptune came out at 28mm diameter.  No problem thought I.  I’ll just roll it out again into a big long sausage; cut it into two equal lengths and have a Neptune and a Uranus, but they only dropped to around 22mm.  A further performance still didn’t give me two sets of 14mm Neptune and Uranus.  What had I forgotten from my school geometry, and what fraction of the 28mm Neptune should I have taken to make a 14mm Neptune?  

In case you were wondering.  No, we didn’t lay it out as far a Neptune at around 1423m, we stopped at Saturn at 474m.  Nevertheless, we calculated we still managed to walk about 8km during the day. DaveP