Find the volume of the right rectangular prism using the cube method Each cube is 1 over 3 inch on each side. What is the volume of the prism? Provide your answer as a fraction reduced to the lowest terms
Since each cube is 1/3 inch on each side, the volume of each cube is (1/3)^3 = 1/27 cubic inches.
We can use the cube method to find the volume of the rectangular prism by counting the number of cubes that fill the space.
Let's label the dimensions of the rectangular prism as length (l), width (w), and height (h). We'll also assume that the rectangular prism has whole number dimensions.
The number of cubes along the length is l/(1/3) = 3l.
The number of cubes along the width is w/(1/3) = 3w.
The number of cubes along the height is h/(1/3) = 3h.
So the total number of cubes needed to fill the rectangular prism is 3l x 3w x 3h = 27lwh.
Therefore, the volume of the right rectangular prism is:
27lwh x volume of each cube = (27lwh) x (1/27)
The factor of 27 cancels out, so the volume is simply:
lwh
Therefore, the volume of the right rectangular prism is lwh cubic inches, or equivalently, lwh/1 cubic inches. This is already in the lowest terms.