(ii) The diameter of a copper sphere is 6 cm . The sphere is melted and drawn into a lor wire with a uniform circular cross-section. If the length of the wire is 36 cm , calcula its curved surface area. (iii) The diameter of a sphere is 6 cm . It is melted and drawn into a wire with a diameter 0.2 cm . Calculate the wire's length.

Let's solve each part step by step. --- ### **Part (ii): Calculating the Curved Surface Area of the Wire** **Given:** - Diameter of the copper sphere = 6 cm - Radius of the sphere, \( r_{\text{sphere}} = \frac{6}{2} = 3 \) cm - Length of the wire, \( L = 36 \) cm **Steps:** 1. **Calculate the Volume of the Sphere:** \[ V_{\text{sphere}} = \frac{4}{3} \pi r_{\text{sphere}}^3 = \frac{4}{3} \pi (3)^3 = 36\pi \, \text{cm}^3 \] 2. **Equate the Volume of the Sphere to the Volume of the Wire (Cylinder):** \[ V_{\text{wire}} = \pi R^2 L \] \[ 36\pi = \pi R^2 \times 36 \] \[ R^2 = 1 \quad \Rightarrow \quad R = 1 \, \text{cm} \] 3. **Calculate the Curved Surface Area of the Wire:** \[ \text{Curved Surface Area} = 2\pi R L = 2\pi \times 1 \times 36 = 72\pi \, \text{cm}^2 \] **Answer for Part (ii):** \[ \text{Curved Surface Area} = 72\pi \, \text{cm}^2 \approx 226.195 \, \text{cm}^2 \] --- ### **Part (iii): Calculating the Length of the Wire** **Given:** - Diameter of the sphere = 6 cm - Radius of the sphere, \( r_{\text{sphere}} = 3 \) cm - Diameter of the wire = 0.2 cm - Radius of the wire, \( r_{\text{wire}} = \frac{0.2}{2} = 0.1 \) cm **Steps:** 1. **Calculate the Volume of the Sphere:** \[ V_{\text{sphere}} = \frac{4}{3} \pi r_{\text{sphere}}^3 = \frac{4}{3} \pi (3)^3 = 36\pi \, \text{cm}^3 \] 2. **Set the Volume of the Sphere Equal to the Volume of the Wire (Cylinder) and Solve for Length \( L \):** \[ V_{\text{wire}} = \pi r_{\text{wire}}^2 L = 36\pi \] \[ \pi (0.1)^2 L = 36\pi \] \[ 0.01L = 36 \quad \Rightarrow \quad L = 3600 \, \text{cm} \] **Answer for Part (iii):** \[ \text{Length of the Wire} = 3600 \, \text{cm} \quad \text{(or 36 meters)} \] --- ### **Final Answers:** - **(ii)** The curved surface area of the wire is \( 72\pi \) cm². - **(iii)** The length of the wire is **3600 cm**.