The diameter of a sphere is $6\ cm$. It is melted and drawn into a wire of diameter $0.2\ cm$. Find the length of the wire.

 Given:

The diameter of a sphere is $6\ cm$. It is melted and drawn into a wire of diameter $0.2\ cm$. 

To do:

We have to find the length of the wire.

Solution:

Diameter of the sphere $= 6\ cm$

This implies,

Radius of the sphere $(r)=\frac{6}{2}$

$=3 \mathrm{~cm}$

Volume of the sphere $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi(3)^{3}$

$=36 \pi \mathrm{cm}^{3}$

Diameter of the wire drawn $=0.2 \mathrm{~cm}$

This implies,

Radius of the wire $(r_{1})=\frac{0.2}{2}$

$=0.1 \mathrm{~cm}$

$=\frac{1}{10} \mathrm{~cm}$

Let the length of the wire be $h$.

Therefore,

$\pi r^{2} h=36 \pi$

$(\frac{1}{10})^{2} h=36$

$\frac{1}{100} h=36$

$h=36 \times 100$

$h=3600 \mathrm{~cm}$

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Updated on: 10-Oct-2022

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