You find the volume of the right rectangular prism using the formula method and want to check your answer using the cube method. What is the edge length of the cubes you will use? Lengths are given in inches. Provide your answer as a fraction reduced to the lowest terms!
To find the edge length of the cubes to use for the cube method, we need to find the greatest common factor of the dimensions of the rectangular prism.
Let's say the dimensions of the rectangular prism are L, W, and H.
The volume of a rectangular prism is given by the formula:
Volume = L x W x H
Now, we want to find the greatest common factor of L, W, and H.
Let's say GCF is x.
Then, L = x * a
W = x * b
H = x * c
So, the volume can also be calculated as:
Volume = x * a * x * b * x * c
Volume = x^3 * a * b * c
Now, using the cube method, we find the edge length of the cubes by taking the cube root of the volume:
Edge length = (x^3 * a * b * c)^(1/3)
Edge length = x * (a * b * c)^(1/3)
Therefore, the edge length of the cubes you will use for the cube method is the cube root of the volume, which simplifies to the cube root of the volume.