Find the volume of the right rectangular prism using the cube method. Each cube is 1/3 inch on each side. What is the volume of the prism? Provide your answer as a fraction reduced to the lowest terms.

Answer 1

To use the cube method, we divide the rectangular prism into smaller cubes and count the number of cubes that fit inside.

If each cube is 1/3 inch on each side, then the height of the rectangular prism must be a multiple of 1/3 inch. Let's say the height is 3 inches, the length is 6 inches, and the width is 9 inches.

We'll start by dividing the rectangular prism into cubes along the length. We can fit 18 cubes along the length (6 inches ÷ 1/3 inch per cube).

Next, we'll divide the rectangular prism into cubes along the width. We can fit 27 cubes along the width (9 inches ÷ 1/3 inch per cube).

Finally, we'll divide the rectangular prism into cubes along the height. We can fit 9 cubes along the height (3 inches ÷ 1/3 inch per cube).

To find the total number of cubes, we multiply the number of cubes along the length, width, and height: 18 cubes × 27 cubes × 9 cubes = 4,374 cubes.

Each cube has a volume of (1/3 inch)³ = 1/27 cubic inches.

Therefore, the total volume of the rectangular prism is:

4,374 cubes × (1/27 cubic inches per cube) = 162 cubic inches.

The volume of the right rectangular prism is 162/1 cubic inches, or 162 cubic inches.