Final answer:
The unique length of the edge of the cube after slicing 2 inches from a rectangular prism with an original volume of 175 cubic inches is 5 inches. We confirmed this by solving the equation s^3 + s^2 × 2 = 175, which only holds true for s = 5.
Step-by-step explanation:
The question involves finding the edge length of a cube after slicing 2 inches from a rectangular prism such that the remaining shape is a perfect cube, given the original volume was 175 cubic inches.
Let's denote the edge length of the cube as s.
Since the remaining shape is a cube, the volume is s^3. To find the value of s, we first realize that the volume of the original rectangular prism was the volume of the cube plus the volume of the 2-inch slice. The volume of the slice would be s^2 × 2 inches.
Therefore, the original volume 175 = s^3 + s^2 × 2.
To solve this equation, we can try different integer values for s because we know that both terms in the original volume equation are whole numbers.
By trial and error, if s = 5, then the cube's volume is 125 and the volume of the slice is 50 (5^2 × 2), which adds up to 175 cubic inches - the original volume. This shows that the edge of the cube is 5 inches.
This solution is unique as no other whole number satisfies the volume equation.