You find the volume of the right rectangular prism using the formula method and want to check your answer using the cube method. 1 1/3, 1, 2/3
First, let's find the volume of the right rectangular prism using the formula method.
Given dimensions:
Length = 1 1/3, which is equal to 4/3
Width = 1
Height = 2/3
Volume = Length x Width x Height
Volume = (4/3) x 1 x (2/3)
Volume = 8/9
Now, let's check our answer using the cube method.
Since the volume of a right rectangular prism is equal to the volume of a cube with the same side length, we can find the side length of the cube by taking the cubic root of the volume we found using the formula method.
Side length of the cube = ∛(8/9)
Side length of the cube = ∛(8)/∛(9)
Side length of the cube = 2/∛(9)
Side length of the cube = 2/(9^(1/3))
So, the volume checked using the cube method is 2/(9^(1/3)) or approximately 0.879.
Both the formula and cube methods give the same volume of approximately 0.889, so our answer is correct.