Question

The diameter of a copper sphere is $6$ cm. The sphere is melted and drawn into a wire of uniform circular cross-section which is $72$ cm long. The diameter of the wire is nearly

• A. $2.8$ cm
• B. $2.7$ cm
• C. $1.4$ cm
• D. None of these

Answer 1

The correct option is C $1.4$ cm

Since, the material of copper sphere is used to make a cylindrical wire

$\therefore$ Volume of wire $=$ Volume of sphere

$\Rightarrow \pi r^2\times 72=\frac{4}{3}\pi \times 3^3$ $[\because$ Volume of cylinder $=\pi r^{2}h$ and Volume of sphere $=\frac{4}{3}\pi r^3]$
$\Rightarrow r=\frac{1}{\sqrt{2}}\text{cm}$
Thus diameter$\frac{2}{\sqrt{2}}\text{cm}=\sqrt{2}\text{cm}=1.4\text{cm}$