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 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.