A solid box is $15$ cm by $10$ cm by $8$ cm. A new solid is formed by removing a cube $3$ cm on a side from each corner of this box. What percent of the original volume is removed?
The volume of the original box is $15\cdot10\cdot8=1200.$ The volume of each cube that is removed is $3\cdot3\cdot3=27.$ Since there are $8$ corners on the box, $8$ cubes are removed. So the total volume removed is $8\cdot27=216$. Therefore, the desired percentage is $\frac{216}{1200}\cdot100 = \fbox{18}.$