To determine which box can hold all the cubes, we need to calculate the volume of each box and compare it to the volume occupied by the cubes.
The volume of a rectangular box is calculated by multiplying its length, width, and height.
Box A:
Volume = 4" x 6" x 8" = 192 cubic inches
Box B:
Volume = 6" x 3" x 12" = 216 cubic inches
Box C:
Volume = 6" x 6" x 4" = 144 cubic inches
Since the cubes have a side length of 1 inch, the volume occupied by 200 cubes would be:
Volume of cubes = 200 cubic inches
Comparing the volumes, we find that:
- Box A has a volume of 192 cubic inches, which is less than the volume of the cubes.
- Box B has a volume of 216 cubic inches, which is greater than the volume of the cubes.
- Box C has a volume of 144 cubic inches, which is less than the volume of the cubes.
Therefore, the box that would be able to hold all 200 cubes is Box B: 6" x 3" x 12".