1. **Problem 16:** Find the height of a right pyramid with volume 72 m³ and base dimensions 800 cm by 300 cm. 2. **Formula:** The volume $V$ of a pyramid is given by $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ 3. **Convert units:** Base dimensions are in cm, convert to meters: $$800\text{ cm} = 8\text{ m}, \quad 300\text{ cm} = 3\text{ m}$$ 4. **Calculate base area:** $$\text{Base Area} = 8 \times 3 = 24\text{ m}^2$$ 5. **Use volume formula to find height $h$:** $$72 = \frac{1}{3} \times 24 \times h$$ 6. **Solve for $h$:** $$72 = 8h \implies h = \frac{72}{8} = 9\text{ m}$$ --- 7. **Problem 17:** Find the volume of water stored in a bin half full. The bin has a cylindrical bottom radius 2 m, height 5 m, and a conical top height 1 m. Total height 6 m. 8. **Calculate volume of cylinder:** $$V_{cyl} = \pi r^2 h = \pi \times 2^2 \times 5 = 20\pi\text{ m}^3$$ 9. **Calculate volume of cone:** $$V_{cone} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \times 2^2 \times 1 = \frac{4}{3}\pi\text{ m}^3$$ 10. **Total volume:** $$V_{total} = 20\pi + \frac{4}{3}\pi = \left(20 + \frac{4}{3}\right)\pi = \frac{64}{3}\pi\text{ m}^3$$ 11. **Half full volume:** $$V_{half} = \frac{1}{2} \times \frac{64}{3}\pi = \frac{32}{3}\pi\text{ m}^3$$ 12. **Convert to liters:** $$1\text{ m}^3 = 1000\text{ L} \implies V_{half} = \frac{32}{3}\pi \times 1000 \approx 33510.32\text{ L}$$ **Final answers:** - Height of pyramid: $9$ m - Water volume half full: approximately $33510$ liters