SOLUTION: a cylinder just fits into a cube of side length 36m calculate the precentage of empty space in the box

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Question 1173726: a cylinder just fits into a cube of side length 36m calculate the precentage of empty space in the box
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The edge of the cube is 36; the volume of the cube is

e%5E3+=+36%5E3

Since the cylinder just fits inside the cube, its height is 36 and its radius is 18; its volume is

%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%2818%5E2%29%2836%29

The volume of empty space is the difference between the two volumes; the percentage of empty space is the ratio of the volume of empty space to the volume of the cube.

You can do the calculations....

Note that the heights of the cube and cylinder are the same; so the ratio of volumes of the two solids is the same as the ratio of the cross sections of the two solids, which is

%28%28pi%29%28%2836%2F2%29%5E2%29%29%2F%2836%5E2%29+=+pi%2F4

So the percentage of empty space is the ratio

%281-pi%2F4%29

converted to a percentage.