A PACKING PUZZLE

As we all know by experience, considerable ingenuity is often required in packing articles into a box if space is not to be unduly wasted. A man once told me that he had a large number of iron balls, all exactly two inches in diameter, and he wished to pack as many of these as possible into a rectangular box `24` `9/10` inches long, `22` `4/5` inches wide, and `14` inches deep. Now, what is the greatest number of the balls that he could pack into that box?