Question

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is:

• A. 12 m
• B. 18 m
• C. 36 m
• D. 66 m

Answer 1

The correct option is C 36 m

Diameter of metallic sphere$=6cm$
$\therefore$ Radius of metallic sphere$=3cm$
Also, we have diameter of cross-section of cylindrical wire$=0.2cm$
$\therefore$ Radius of cross-section of cylinrical wire$=0.1cm$
Let the length of the wire be $hcm$
Since metallic sphere is converted into a cylinder shaped wire of length $hcm$
$\therefore$ Volume of the metal used in wire = Volume of the sphere

$\pi \times r_s^2\times h=\frac{4}{3}\times \pi \times r_c^3$

$\Rightarrow \pi \times (\frac{1}{10}{)}^2\times h=\frac{4}{3}\times \pi \times 27$

$\Rightarrow \pi \times \frac{1}{100}\times h=36\pi$

$\therefore h=\frac{36\pi \times 100}{\pi }cm=3600cm=36metres$