1. **Problem statement:** Calculate the volume of a round wading pool with diameter 125 cm and height 30 cm. Then find the water height if the pool contains 200 liters. 2. **Formula for volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate radius:** Diameter $= 125$ cm, so radius $r = \frac{125}{2} = 62.5$ cm. 4. **Calculate volume in cubic centimeters:** $$V = \pi \times (62.5)^2 \times 30$$ $$= \pi \times 3906.25 \times 30$$ $$= \pi \times 117187.5$$ $$\approx 3.1416 \times 117187.5 = 368141.59 \text{ cm}^3$$ 5. **Convert volume to liters:** Since $1$ liter $= 1000$ cm$^3$, $$V = \frac{368141.59}{1000} = 368.14 \text{ liters}$$ 6. **Compare with advertised volume:** Advertised volume is 200 liters, which is less than the full volume. 7. **Find water height $h_w$ for 200 liters:** Use volume formula with unknown height: $$200 = \pi \times (62.5)^2 \times h_w / 1000$$ Multiply both sides by 1000: $$200 \times 1000 = \pi \times 3906.25 \times h_w$$ $$200000 = \pi \times 3906.25 \times h_w$$ Divide both sides by $\pi \times 3906.25$: $$h_w = \frac{200000}{\pi \times 3906.25}$$ Show cancellation: $$h_w = \frac{200000}{\cancel{\pi} \times 3906.25} \times \frac{\cancel{\pi}}{\cancel{\pi}} = \frac{200000}{\pi \times 3906.25}$$ Calculate: $$h_w \approx \frac{200000}{3.1416 \times 3906.25} = \frac{200000}{12269.0} \approx 16.3 \text{ cm}$$ 8. **Final answers:** - Full volume: approximately 368 liters - Water height for 200 liters: approximately 16 cm These match the provided facit values 368 and 16.