Final answer:
The side length of the original cube is 3 inches.
The correct answer is a.
Step-by-step explanation:
To find the side length of the original cube, we need to use the given information. Let's call the side length of the original cube 'x'. When a 5-inch thick slice is cut off the top of the cube, the resulting rectangular box has a volume of 75 in^3. This rectangular box is formed by a base with length and width 'x' and a height of 5 inches.
The volume of a rectangular box is given by V = length x width x height. So, we have the equation 75 = x * x * 5. Solving for x, we find that the side length of the original cube is approximately 3 inches. Therefore, the correct option is a. 3 inches.