Question

The diameter of a metallic sphere is $6cm$. It is melted and drawn into a wire of diameter $2cm$, then the length of the wire is

• A. $12cm$
• B. $18cm$
• C. $36cm$
• D. $66cm$

Answer 1

Answer: (C)

$36cm$

Diameter of sphere $=6$ cm

Radius of sphere $=\frac{6}{2}=3cm$

Volume of sphere $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 3\times 3\times 3=36\pi {cm}^3$

Let the length of wire be $h$ cm

Diameter of wire $=2$ cm

Radius of wire $=\frac{2}{2}=1cm$

As the wire is in the shape of cylinder .so that volume of cylinder $=\pi r^{2}h$

Now, volume of metal sphere $=$ volume of wire

$36\pi =\pi \times 1^2\times hh=36cm$