<PRE><B>Question 1173726</B>
&lt;br&gt;
The edge of the cube is 36; the volume of the cube is&lt;br&gt;
{{{e^3 = 36^3}}}&lt;br&gt;
Since the cylinder just fits inside the cube, its height is 36 and its radius is 18; its volume is&lt;br&gt;
{{{(pi)(r^2)(h) = (pi)(18^2)(36)}}}&lt;br&gt;
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.&lt;br&gt;
You can do the calculations....&lt;br&gt;
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&lt;br&gt;
{{{((pi)((36/2)^2))/(36^2) = pi/4}}}&lt;br&gt;
So the percentage of empty space is the ratio&lt;br&gt;
{{{(1-pi/4)}}}&lt;br&gt;
converted to a percentage.&lt;br&gt;
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