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 fit in the prism.

We start with the length of the prism, which is 6 inches. We divide this by the length of each cube, which is 1/3 inch.

6 ÷ 1/3 = 18

So there are 18 cubes along the length of the prism.

Next, we do the same for the width, which is 4 inches.

4 ÷ 1/3 = 12

So there are 12 cubes along the width.

Finally, we do this for the height, which is 5 inches.

5 ÷ 1/3 = 15

So there are 15 cubes along the height.

To find the volume of the prism, we multiply the number of cubes in each dimension:

18 × 12 × 15 = 3,240

However, we need to remember that each cube has a side length of 1/3 inch, so we need to convert this to cubic inches:

3,240 × (1/3)^3 = 3,240 × 1/27 = 120

Therefore, the volume of the right rectangular prism is 120 cubic inches, which can also be written as 40/3 cubic inches in the lowest terms.