Question
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?
Answers
GPT 3.5
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.
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.