- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
A copper rod of diameter \( 1 \mathrm{~cm} \) and length \( 8 \mathrm{~cm} \) is drawn into a wire of length \( 18 \mathrm{~m} \) of uniform thickness. Find the thickness of the wire.
Given:
A copper rod of diameter \( 1 \mathrm{~cm} \) and length \( 8 \mathrm{~cm} \) is drawn into a wire of length \( 18 \mathrm{~m} \) of uniform thickness.
To do:
We have to find the thickness of the wire.
Solution:
Diameter of the rod $=1 \mathrm{~cm}$
This implies,
Radius of the cone $\mathrm{R}=\frac{1}{2} \mathrm{~cm}$
Height of the cone $H=8 \mathrm{~cm}$
Therefore,
Volume of the cone $=\pi \mathrm{R}^{2} H$
$=\pi \times(\frac{1}{2})^{2} \times 8 \mathrm{~cm}^{3}$
$=\pi \times \frac{1}{4} \times 8$
$=2 \pi \mathrm{cm}^{3}$
Length of the wire drawn $h=18 \mathrm{~m}$
$=1800 \mathrm{~cm}$
Let the radius of the wire be $r$.
Therefore,
Volume of the wire $=\pi r^{2} h$
$=\pi r^{2} \times 1800$
$\Rightarrow 1800 \pi r^{2}=2 \pi$
$\Rightarrow r^{2}=\frac{2 \times \pi}{1800 \times \pi}$
$\Rightarrow r^{2}=\frac{1}{900}$
$\Rightarrow r^{2}=(\frac{1}{30})^{2}$
$\Rightarrow r=\frac{1}{30} \mathrm{~cm}$
$\Rightarrow r=\frac{100}{30} \mathrm{~mm}$
$\Rightarrow r=\frac{10}{3} \mathrm{~mm}$
This implies,
Diameter of the wire $=2 r$
$=2 \times \frac{10}{3}$
$=\frac{20}{3}$
$=6.67 \mathrm{~mm}$
The thickness of the wire is $6.67\ mm$.