SOLUTION: Sarah buys her friend, Alyssa, a birthday present. She decides to mail her a bowling ball. The bowling ball fits tightly into a box that is a cube. Sarah would like to fill the ext

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Question 831364: Sarah buys her friend, Alyssa, a birthday present. She decides to mail her a bowling ball. The bowling ball fits tightly into a box that is a cube. Sarah would like to fill the extra space in the box with foam packing material.
What percent of the volume (space) of the box that remains and needs to be filled with the packing material?
*I don't know how to start this problem. The problem doesn't state the radius or diameter. Any help is greatly appreciated*
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
R=radius of .
Since the ball fits tightly in the cube shaped box, the inside of the box must be 2R wide.
Volume of the ball =%284%2F3%29pi%2AR%5E3
Volume inside the box =%282R%29%5E3=8R%5E3
The volume that needs to be filled with packing material is
8R%5E3-%284%2F3%29pi%2AR%5E3=%288-4pi%2F3%29R%5E3
As a fraction of the volume inside the box that is
%288-4pi%2F3%29R%5E3%2F8R%5E3=%288-4pi%2F3%29%2F8=1-pi%2F6
That is approximately 0.4764 , which is 47.64%.

It does not matter what size ball you fit tightly into a cube box, about 48% of the box will be empty space.