A solid metallic cone of radius 10 cm and height 12 cm is melted to form a wire of uniform cross-section 1 cm². The length of wire formed is :

1. 40 × π cm

2. 4 × π m

3. 400 × π m

4. 2 × π m

Given,

A solid metallic cone of radius (r) 10 cm and height (h) 12 cm is melted to form a wire of uniform cross-section 1 cm².

Let length of wire formed be l cm.

∴ Volume of cone = Volume of wire

$\Rightarrow \dfrac{1}{3}πr^2h = \text{Area of cross-section × length} \\[1em] \Rightarrow \dfrac{1}{3}π \times 10^2 \times 12 = 1 \times l \\[1em] \Rightarrow l = 4 \times π \times 10^2 \\[1em] \Rightarrow l = 400 π \text{ cm} \\[1em] \Rightarrow l = \dfrac{400π}{100} \text{ m} \\[1em] \Rightarrow l = 4 × π \text{ m}.$

Hence, Option 2 is the correct option.