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.
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.