1. **Problem statement:** We have a cylinder with diameter 7 cm and height 9 cm. (a) Find the width $w$ of the rectangle in the net of the cylinder. (b) Calculate the area of the curved surface of the cylinder. 2. **Formulas and rules:** - The width $w$ of the rectangle in the net corresponds to the circumference of the circular base of the cylinder. - The circumference $C$ of a circle is given by $$C = \pi d$$ where $d$ is the diameter. - The curved surface area $A$ of a cylinder is given by $$A = \text{circumference} \times \text{height} = C \times h$$ 3. **Calculations:** (a) Calculate the width $w$: $$w = C = \pi \times 7 = 7\pi$$ Using $\pi \approx 3.1416$: $$w \approx 7 \times 3.1416 = 21.9912$$ Rounded to the nearest integer: $$w \approx 22 \text{ cm}$$ (b) Calculate the curved surface area: $$A = C \times h = 7\pi \times 9 = 63\pi$$ Using $\pi \approx 3.1416$: $$A \approx 63 \times 3.1416 = 197.9208$$ Rounded to the nearest integer: $$A \approx 198 \text{ cm}^2$$ **Final answers:** - Width $w$ of the rectangle: **22 cm** - Curved surface area: **198 cm$^2$**