Question

A solid lead ball of radius $6cm$ is melted and then drawn into a wire of diameter $0.2cm$. The length of wire is

$\left(a\right)272m\left(b\right)288m\left(c\right)292m\left(d\right)296m$

Answer 1

ANSWER:
(b) $288m$
From question,
Radius of lead ball $=6cm$
Diameter of wire $=0.1cm$
So, radius of wire $=\frac{0.2cm}{2}=0.1cm$
Let $hmetre$ be the length of wire.
Volume of the lead ball = volume of the wire
$⟹\frac{4}{3}\pi r^3=\pi r^{2}h$
$⟹\frac{4}{3}\pi \times 6^3=\pi \times {0.1}^{2}h$
$⟹\frac{4}{3}\times 216=0.01h$
$⟹4\times 72=0.01h$
$⟹h=\frac{4\times 72}{0.01}cm$
$⟹h=\frac{288}{0.01}cm$
$⟹h=\frac{288}{0.01}\times \frac{1}{100}m[\because 1cm=\frac{1}{100}m]$
$⟹h=\frac{288}{0.01\times 100}m$
$⟹h=288m$
Therefore, the length of the wire is $288m$.