Question

A box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.

If the length and width of the base are doubled, how many cubes could the new box hold?

18
24
48
96

Answer 1

A 6-inch cube fits 2 across a 12-inch side, 3 across an 18-inch side, and 2 across the 12-inch height, so the original box holds 2×3×2 = 12 cubes. Doubling the base dimensions makes those counts 4 and 6, so the new box holds 4×6×2 = 48 cubes.

Answer: 48.