Kim wants to use cubes that are all the same size to fill a box that measures 3 1/2 ft x 3 1/4 ft x 2 ft without gaps. He has 1/2 ft cubes, 1/4 ft cubes, and 1 ft cubes. Which cubes should he use? Explain?

Answer: he should use 1/2 ft cubes and 1/4 ft cubes.

Step-by-step 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.