SOLUTION: Six squash balls are packaged in a cylindrical container. Calculate the volume of air inside the container in terms of the radius r.

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Question 752554: Six squash balls are packaged in a cylindrical container. Calculate the volume of air inside the container in terms of the radius r.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
We are assuming that the six squash balls fit snugly (no wiggle room) inside the cylindrical container.
The volume of the cylindrical container is given by:
V+=+%28pi%29r%5E2h where r = the radius of the cross-section of the cylindrical container.
Since the six balls fit snugly inside the cylindrical container, the radius of each ball must be the same as the radius of the cylindrical container.
Therefore, the height of the cylindrical container must be equal to six times the diameter of one ball or 12 time the radius of each ball.
So we can write the volume of the cylinder as:
V+=+%28pi%29r%5E2%2812r%29 or V+=+12%28pi%29r%5E3
The volume of one ball (a sphere of radius r) is:
v+=+%284%2F3%29%28pi%29r%5E3 so six times this is:
v+=+6%284%2F3%29%28pi%29r%5E3 or
v+=+8%28pi%29r%5E3 The volume of air in the container with the six balls inside is found by subtracting the volume of the six balls from the volume of the empty cylindical container, thus:
12%28pi%29r%5E3+-+8%28pi%29r%5E3=4%28pi%29r%5E3