1. **Problem (a):** Find the volume of a solid cylinder with height and diameter both 9 cm. 2. **Formula:** The volume of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Step 1:** Calculate the radius. Since diameter $d = 9$ cm, radius $r = \frac{d}{2} = \frac{9}{2} = 4.5$ cm. 4. **Step 2:** Substitute values into the volume formula: $$V = \pi \times (4.5)^2 \times 9$$ 5. **Step 3:** Calculate the square of the radius: $$4.5^2 = 20.25$$ 6. **Step 4:** Multiply: $$V = \pi \times 20.25 \times 9 = \pi \times 182.25$$ 7. **Answer (a):** The volume of the cylinder is $$182.25\pi \text{ cm}^3$$. 8. **Problem (b)(i):** Find the area of a square lawn with perimeter 96 m. 9. **Formula:** The perimeter of a square is $$P = 4s$$ where $s$ is the side length. 10. **Step 1:** Find the side length: $$s = \frac{P}{4} = \frac{96}{4} = 24 \text{ m}$$ 11. **Step 2:** Calculate the area of the square: $$A = s^2 = 24^2 = 576 \text{ m}^2$$ 12. **Answer (b)(i):** The area of the lawn is $$576 \text{ m}^2$$. 13. **Problem (b)(ii):** Calculate the curved surface area of a cylindrical roller with width 1 m and diameter 75 cm. 14. **Note:** Width corresponds to height $h = 1$ m. Diameter $d = 75$ cm = 0.75 m. 15. **Formula:** Curved surface area of a cylinder is $$A = 2 \pi r h$$. 16. **Step 1:** Calculate radius: $$r = \frac{d}{2} = \frac{0.75}{2} = 0.375 \text{ m}$$ 17. **Step 2:** Substitute values: $$A = 2 \pi \times 0.375 \times 1 = 0.75\pi$$ 18. **Step 3:** Calculate numerical value: $$A \approx 0.75 \times 3.1416 = 2.3562 \text{ m}^2$$ 19. **Step 4:** Round to one decimal place: $$A \approx 2.4 \text{ m}^2$$ 20. **Answer (b)(ii):** The curved surface area is approximately $$2.4 \text{ m}^2$$.