Final answer:
To determine the number of 2-inch cubes needed to fill the cubic box with edge lengths of 8 inches, calculate the volume of the box and divide it by the volume of each cube. The answer is 64 cubes (Option A).
Step-by-step explanation:
To determine the number of 2-inch cubes needed to fill the cubic box with edge lengths of 8 inches, we need to calculate the volume of the box and then divide it by the volume of each cube. The volume of the box is given by the formula: Volume = length x width x height. Substituting the given values, we get: Volume = 8 inches x 8 inches x 8 inches = 512 cubic inches. The volume of each cube is given by the formula: Volume = length x width x height. Substituting the given values, we get: Volume = 2 inches x 2 inches x 2 inches = 8 cubic inches. Now, divide the volume of the box by the volume of each cube to get the number of cubes needed: 512 cubic inches ÷ 8 cubic inches = 64 cubes. Therefore, the answer is A) 64 cubes.