Eight wooden spheres with radii of 3 inches are packed snuggly into a cube-shaped box 12 inches on one side. The remaining space is filled with packing beads. What is the volume occupied by the packing beads?

Answer 1

The total volume of the cube-shaped box is 12^3 = 1728 cubic inches.

The volume of each wooden sphere is calculated as 4/3 * π * r^3 = 4/3 * 3.14 * 3^3 = 113.04 cubic inches.

The total volume taken up by the eight wooden spheres is 8 * 113.04 = 904.32 cubic inches.

Therefore, the volume occupied by the packing beads is 1728 - 904.32 = 823.68 cubic inches.