Asked by AP Physics

Again Chapter one Stuff...

Discuss how the notion of symmetry could be used to estimate the number of marbles in a one-liter jar.

I'm lost I'm thinkthing somewer along the lines of counting them up nice and simple but I have no idea

Answers

Answered by MathMate
The only relevance of symmetry I can think of is the following, basically subdividing the litre jar into 8 smaller pieces, a little easier to calculate.

A litre jar has a capacity of 1000 cm<sup>3</sup>.
If we look at symmetry in the x-y, y-z and z-x planes, we basically cut up the volume into 8 parts, each of which has 125 cm<sup>3</sup>, or the equivalent of a 5 cm. cube.
If we think of a marble as a sphere of 1 cm diameter, we can squeeze in 5*5*5=125 marbles in each of the subdivided cubes. Hence for the litre jar, we can probably squeeze in 1000 marbles.

Tell us what you think.
(sorry I probably won't be here to answer you tomorrow morning, but other teachers can help you out)

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