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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?