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 find the volume of the right rectangular prism using the cube method, we can divide it into smaller cubes and count them.

Let's say the dimensions of the prism are x, y, and z, where x is the length, y is the width, and z is the height. We can divide each dimension by 1/3 inch to get the number of cubes in each direction:

Number of cubes in the x direction = x / (1/3) = 3x
Number of cubes in the y direction = y / (1/3) = 3y
Number of cubes in the z direction = z / (1/3) = 3z

Therefore, the total number of cubes in the prism is:

Number of cubes = (3x) * (3y) * (3z) = 27xyz

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

Volume = (27xyz) * (1/27) = xyz

Therefore, the volume of the prism is xyz, which is a fraction that cannot be reduced further.