MHB How many marbles are in a jar?

[Max CR]

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?

 

[Max CR]

I have figured out the problem. Thank you.