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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 use the cube method to check the volume of a right rectangular prism, you divide the prism into smaller cubes of equal volume. The edge length of these cubes is a common factor of all three dimensions of the prism.
Let's say the dimensions of the right rectangular prism are length = L, width = W, and height = H. Then its volume V can be found using the formula V = LWH.
To find the edge length of the cubes we'll use in the cube method, we need to find the greatest common factor (GCF) of L, W, and H. One way to do this is to factor each dimension into primes and then take the product of the common factors with the smallest exponent for each prime.
For example, let's say L = 9, W = 12, and H = 15. Then we can factor each dimension as follows:
L = 3 x 3
W = 2 x 2 x 3
H = 3 x 5
To find the GCF, we take the product of the common factors with the smallest exponent for each prime, which is:
GCF = 3 x 3 x 5 = 45
Therefore, the edge length of the cubes we'll use in the cube method is 45/45 = 1 inch.