Six spherical cannon balls are tightly packed into a rectangular box in one layer. Each row has two cannon balls and each column has three. What part of the box is empty?

To answer this question, we need to understand the packing efficiency of spheres.

1. First, we need to know that the most efficient way to pack spheres (like cannon balls) is in a hexagonal close-packed arrangement. This arrangement fills about 74% of the space.

2. However, in this case, the cannon balls are packed in a rectangular box, not in a hexagonal arrangement. Therefore, the packing efficiency will be less than 74%.

3. In a rectangular arrangement, spheres fill about 52.4% of the space. This is because each sphere occupies a volume of 4/3πr³ (where r is the radius of the sphere), but is contained within a box that has a volume of (2r)³ = 8r³. The ratio of these two volumes is (4/3πr³) / (8r³) = π/6 ≈ 0.524.

4. Therefore, about 47.6% of the box will be empty.