SOLUTION: A dozen golf balls fit inside the shape of a rectangular prism. The golf balls are packed tightly together and they touch top, bottom and side of the box. What percentage of the

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Question 475300: A dozen golf balls fit inside the shape of a rectangular prism. The golf balls are packed tightly together and they touch top, bottom and side of the box. What percentage of the volume within the box is air?
I have the answer but have no idea how they arrived at it.
Air would accupy 47.6 percent of the volume of the box. (100-52.4=47.6)
How can you get this answer when the question give no numbers?
Answer by ccs2011(207) (Show Source):
You can put this solution on YOUR website!
Even though they don't give any numbers, they do give reference points:
Shape is rectangular prism: Volume = length*width*depth
Golf balls are like spheres: Volume =
Remember the goal isn't to determine the actual volume just comparing the volume the golf balls take up with the volume of the entire box.
Percentage is just a ratio.
Now every golf ball is identical in size, so the radius is constant.
Since we do not know the radius our volumes will be in terms of r.
The volume of 12 golf balls =
Now the tricky part is getting the volume of the box in terms of r.
Now the dimensions of this box can be anything as long as it holds 12 golf balls perfectly. The easiest thing to do is imagine a long sleeve where all 12 balls are stacked on top of each other. Then it is 12 golf balls high, and length and width is same as length of 1 golf ball. Now remember that length of a circle is the diameter which is twice the radius.
Now we know the dimensions:
length = width = 2r
depth = 12*2r = 24r
Volume =
Now the ratio of golf balls volume to box volume is:

So 52.4% of the box is taken up by the golf balls.
Leaving 47.6% of the box to be taken up by air.
Hope that helped :)