How many marbles are in a jar?

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SUMMARY

The discussion centers on calculating the number of marbles in a jar, concluding that while mathematical calculations suggest there could be 262 marbles based on the volume of the jar and the volume of a single marble, the actual count is 167 marbles. The discrepancy arises from the assumption that the jar is uniformly filled, neglecting the irregular packing of the marbles. The volume calculations used include the formula for the volume of a sphere and a cylinder, with specific dimensions provided for both.

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How many marbles are in a jar?

There are about 167 marbles in a jar.

Volume of sphere (marbles) = (4/3)πr^3
r = (4/3)π(0.25)^3
volume of sphere/marble = 0.0654 inches

Volume of cylinder (glass) = v=πr^2h
v=π(1.625)^2*2.80
volume of cylinder/glass = 23.23 inches

It is a given that the glass is 74% filled and 26% empty due to space in between the marbles.

Number of marbles = (jar volume * 0.74)/volume of one marble
= (23.23*0.74)/0.0654
= 262 marbles
Math says that there is 262 marbles when it is actually 167 marbles. Any ideas?
 
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I have figured out the problem. Thank you.
 

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