Question

If the sphere of radius 6 cm is melted and drawn into a wire of radius 0.2 cm, then the length of the wire is

• A. 75 m
• B. 72 cm
• C. 72 m
• D. 75 cm

Answer 1

The correct option is C 72 m

Given that, a sphere of radius $6cm$ and radius of wire $0.2cm$.

Let, length of wire is $=l$

Now,

Volume of wire=volume of the sphere

$\pi r^{2}h=\frac{4}{3}\pi R^3$

$r^{2}h=\frac{4}{3}{R}^3$

${\left(0.2\right)}^{2}h=\frac{4}{3}{.6}^3$

$h=\frac{6\times 6\times 2\times 4}{0.2\times 0.2}=\frac{288\times 100}{4}=72\times 100$

$h=7200cm$

$h=72m$

Hence, this is the answer.