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Marbles are considered spheres, and there's a mathematical rule to define the random close-packing of spheres in a confined space. Basically:
- Calculate the volume of a single marble (using the formula Vmarble= 4/3πr3 to determine the volume of the sphere from its radius, which is half its diameter).
- Then calculate the internal volume of the jar, using the formula Vjar= πr2h for calculating the volume of a cylinder.
- Divide Vjar by Vmarble; then multiply by .6, as this represents how much of the space inside the jar is (probably) filled with marbles. In other words, N ≈ .6 (Vjar/Vmarble). (Obviously, N then needs to be rounded off to the nearest whole number.)
Or if this is too much work, you can try counting the number of marbles at the bottom (or at the top), and then counting the number of rows there appear to be. Either way, good luck.
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