Answer: he should use 1/2 ft cubes and 1/4 ft cubes.
Explanation:
The dimensions of the large box that Kim wants to fill are
3 1/2 ft x 3 1/4 ft x 2 ft
The formula for determining the volume of a cuboid is expressed as
Volume = length × width × height
Volume of the box = 3.5 × 3.25 × 2 = 22.75 ft³
The formula for determining the volume of a cube is expressed as
Volume = s³
1) Volume of the cube whose side length is 0.5 ft is 0.5³ = 0.125ft³
Number of this cubes that he would use to fill the box is
22.75/0.125 = 182 cubes
Since it is a whole number, then it can fill the box without gaps.
2) Volume of the cube whose side length is 0.25 ft is 0.25³ = 0.015625ft³
Number of this cubes that he would use to fill the box is
22.75/0.015625 = 1456 cubes
Since it is a whole number, then it can fill the box without gaps.
3) Volume of the cube whose side length is 1 ft is 1³ = 1ft³
Number of this cubes that he would use to fill the box is
22.75/1 = 22.75 cubes
Since it is not a whole number, then there would be gaps.