SOLUTION: You have a cylinder that has a 14 inch diameter and is 17 inches tall. You fill the cylinder with 100 marbles. Each marble has a diameter of 2. How much air will be left in the cyl

Algebra ->  Volume -> SOLUTION: You have a cylinder that has a 14 inch diameter and is 17 inches tall. You fill the cylinder with 100 marbles. Each marble has a diameter of 2. How much air will be left in the cyl      Log On


   

Question 1088635: You have a cylinder that has a 14 inch diameter and is 17 inches tall. You fill the cylinder with 100 marbles. Each marble has a diameter of 2. How much air will be left in the cylinder after it is filled with marbles?
Found 3 solutions by Fombitz, addingup, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the volume of the cylinder.
Find the volume of a marble.
Subtract 100 marble volumes from the cylinder volume.
V%5Bcyl%5D=pi%28D%5E2%2F4%29%2817%29=pi%2814%5E2%2F4%29%2817%29
V%5Bm%5D=%284%2F3%29pi%28D%5E3%2F8%29=%28pi%2F6%29%282%29%5E3
So then,
V%5Bair%5D=V%5Bcyl%5D-100V%5Bm%5D
V%5Bair%5D=pi%2814%5E2%2F4%29%2817%29-800pi%2F6
Work those out for the final answer.

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
(14/2)^2 x Pi x 17 = 2616.95 this is the volume of the cylinder
4/3((2/2)^3)Pi = (4Pi)/3 = 4.189 this is the volume of each marble.
2616.95 - (4.189*100) = 2198.05 is air

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

You have a cylinder that has a 14 inch diameter and is 17 inches tall. You fill the cylinder with 100 marbles. Each marble has a diameter of 2. How much air will be left in the cylinder after it is filled with marbles?
Volume of the cylinder: 833pi

Volume of one marble (sphere): %284%2F3%29pi 

Volume of 100 of THESE marbles: 400pi%2F3

Air left in cylinder that’s filled with 100 of THESE marbles: .