1. **Problem statement:** A metallic spherical shell has an external radius of 6 cm and thickness of 1 cm. It is melted and drawn into a wire of diameter 2 cm. If 1 cm of the wire is sold at 3, find the total price of the wire. 2. **Step 1: Calculate the volume of the spherical shell.** The volume of a spherical shell is given by the difference of volumes of two spheres: $$V = \frac{4}{3}\pi (R^3 - r^3)$$ where $R$ is the external radius and $r$ is the internal radius. Given: $R = 6$ cm Thickness $= 1$ cm, so internal radius $r = R - 1 = 5$ cm Calculate volume: $$V = \frac{4}{3}\pi (6^3 - 5^3) = \frac{4}{3}\pi (216 - 125) = \frac{4}{3}\pi (91) = \frac{364}{3}\pi \text{ cm}^3$$ 3. **Step 2: Calculate the volume of the wire.** The wire is cylindrical with diameter 2 cm, so radius $r_w = 1$ cm. Let the length of the wire be $L$ cm. Volume of wire: $$V = \pi r_w^2 L = \pi (1)^2 L = \pi L \text{ cm}^3$$ 4. **Step 3: Equate volumes to find length $L$.** Since the shell is melted and reshaped into the wire, volumes are equal: $$\pi L = \frac{364}{3}\pi$$ Divide both sides by $\pi$: $$L = \frac{364}{3} = 121.33 \text{ cm}$$ 5. **Step 4: Calculate the price of the wire.** Price per cm of wire = 3 Length of wire = 121.33 cm Total price: $$\text{Price} = 3 \times 121.33 = 364$$ **Final answer:** The wire will fetch 364.