- 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
In a circle of radius \( 6 \mathrm{~cm} \), a chord of length \( 10 \mathrm{~cm} \) makes an angle of \( 110^{\circ} \) at the centre of the circle. Find the area of the sector \( O A B \).
Given:
Radius of the circle $r=6 \mathrm{~cm}$.
Length of the arc $l=10 \mathrm{~cm}$.
Angle subtended at the centre $=110^{\circ}$.
To do:
We have to find the area of the sector \( O A B \).
Solution:
Let $OA$ and $OB$ are the radii of the circle and $AB$ the chord.
We know that,
Area of a sector is $\pi r^{2} (\frac{\theta}{360^{\circ}})$.
Therefore,
Area of the sector $OAB =\pi r^{2} \times \frac{\theta}{360^{\circ}}$
$= 3.14 \times 6 \times 6 \times \frac{110^{\circ}}{360^{\circ}} \mathrm{cm}^{2}$
$=36 \times 3.14 \times \frac{11}{36} \mathrm{~cm}^{2}$
$=34.54 \mathrm{~cm}^{2}$
The area of the sector \( O A B \) is $34.54\ cm^2$.