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 count the number of cubes that can fit inside the rectangular prism.

Let the dimensions of the rectangular prism be l, w, and h. We divide each dimension by 1/3 to determine the number of cubes that can fit in each direction:

- The length l can fit \frac{l}{1/3}=3l cubes.
- The width w can fit \frac{w}{1/3}=3w cubes.
- The height h can fit \frac{h}{1/3}=3h cubes.

Therefore, the total number of cubes that can fit inside the rectangular prism is 3l x 3w x 3h = 27lwh.

Each cube has a volume of (1/3)^3 = 1/27 cubic inches. Therefore, the volume of the rectangular prism is:

27lwh x (1/27) = lwh.

So the volume of the right rectangular prism is lwh expressed as a fraction reduced to the lowest terms.