1. **State the problem:** We have a swimming pool with an inside perimeter of 24 meters and an outside perimeter of 48 meters. We want to find how many stepping stones are needed to cover the area outside the pool if 6 stepping stones cover 1 square meter. 2. **Understand the problem:** The stepping stones cover the area between the inside and outside perimeters, which is the ring-shaped area around the pool. 3. **Assumptions:** The pool and the area outside are shaped such that the perimeters correspond to circles (common assumption for such problems). 4. **Formulas:** - Perimeter (circumference) of a circle: $$P = 2\pi r$$ - Area of a circle: $$A = \pi r^2$$ 5. **Find the radii:** - Inside radius $$r_i$$ from inside perimeter $$P_i = 24$$: $$r_i = \frac{P_i}{2\pi} = \frac{24}{2\pi} = \frac{12}{\pi}$$ - Outside radius $$r_o$$ from outside perimeter $$P_o = 48$$: $$r_o = \frac{P_o}{2\pi} = \frac{48}{2\pi} = \frac{24}{\pi}$$ 6. **Calculate the areas:** - Inside area $$A_i$$: $$A_i = \pi r_i^2 = \pi \left(\frac{12}{\pi}\right)^2 = \pi \frac{144}{\pi^2} = \frac{144}{\pi}$$ - Outside area $$A_o$$: $$A_o = \pi r_o^2 = \pi \left(\frac{24}{\pi}\right)^2 = \pi \frac{576}{\pi^2} = \frac{576}{\pi}$$ 7. **Calculate the ring area (area outside the pool):** $$A_{ring} = A_o - A_i = \frac{576}{\pi} - \frac{144}{\pi} = \frac{432}{\pi}$$ 8. **Calculate the number of stepping stones needed:** - 6 stepping stones cover 1 square meter, so 1 stepping stone covers $$\frac{1}{6}$$ square meters. - Number of stepping stones needed: $$N = A_{ring} \times 6 = \frac{432}{\pi} \times 6 = \frac{2592}{\pi} \approx 825.95$$ 9. **Final answer:** Since we cannot have a fraction of a stepping stone, round up: $$\boxed{826}$$ stepping stones are needed to cover the area outside the swimming pool.