Question

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

Options

• 40 × π cm

• 4 × π m

• 400 × π m

• 2 × π m

Answer 1

4 × π m

Explanation:

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

\[\Rightarrow \frac{1}{3}\, \pi r^2 h = \text{Area of cross-section} \times \text{length}\]

\[\Rightarrow \frac{1}{3}\, \pi \times 10^2 \times 12 = 1 \times l\]

\[\Rightarrow l = 4 \times \pi \times 10^2\]

\[\Rightarrow l = 400\pi\ \text{cm}\]

\[\Rightarrow l = \frac{400\pi}{100}\ \text{m}\]

\[\Rightarrow l = 4 \times \pi\ \text{m}.\]