1. **Problem statement:** A 4 ft thick slice is cut off the top of a cube, producing a rectangular box with volume 67 ft\(^3\). We want to find the side length $s$ of the original cube. 2. **Define variables:** Let $s$ be the side length of the original cube in feet. 3. **Volume of original cube:** The volume is $s^3$. 4. **Dimensions of the sliced box:** Removing a 4 ft thick slice from the top reduces the height by 4 ft, so the box’s dimensions are $s \times s \times (s-4)$. 5. **Volume of the rectangular box:** Given as 67 ft\(^3\). So, $$s \times s \times (s-4) = 67$$ which simplifies to $$s^2 (s-4) = 67$$ 6. **Expand and rewrite:** $$s^3 - 4s^2 = 67$$ 7. **Rewrite as a cubic equation:** $$s^3 - 4s^2 - 67 = 0$$ 8. **Solve for $s$ using graphing calculator or algebraic numeric methods:** Using the ALEKS graphing calculator, find the root of $$f(s) = s^3 - 4s^2 - 67$$ 9. **Approximate solution:** The positive root is approximately $$s \approx 6.31$$ Thus, the side length of the original cube rounded to two decimals is **6.31 ft**.