- Trending Categories
- 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

# Find the area of a sector of a circle with radius 6 cm if angle of the sector is $60^o$.

Given:

Radius of the circle $=6\ cm$.

Angle subtended by the sector $=60^o$

To do:

We have to find the area of the sector.

Solution:

Area of the sector subtending $\theta$ at the centre $=\pi r^{2} \times \frac{\theta}{360^{\circ}}$

Therefore,

Area of the given sector $=\pi(6)^{2} \times \frac{60^{\circ}}{360^{\circ}} \mathrm{cm}^{2}$

$=36 \pi \times \frac{1}{6} \mathrm{~cm}^{2}$

$=6\pi \mathrm{cm}^{2}$

The area of the sector is $6\pi \mathrm{cm}^{2}$.

- Related Articles
- A sector of a circle of radius 4 cm contains an angle of $30^o$. Find the area of the sector.
- A sector of a circle of radius 8 cm contains an angle of $135^o$. Find the area of the sector.
- The area of a sector of a circle of radius \( 2 \mathrm{~cm} \) is \( \pi \mathrm{cm}^{2} \). Find the angle contained by the sector.
- The area of a sector of a circle of radius \( 5 \mathrm{~cm} \) is \( 5 \pi \mathrm{cm}^{2} \). Find the angle contained by the sector.
- Find the area of the minor segment of a circle of radius \( 14 \mathrm{~cm} \), when the angle of the corresponding sector is \( 60^{\circ} . \)
- In a circle of radius 21 cm, an arc subtends an angle of $60^o$ at the centre. Find area of the sector formed by the arc.
- Area of a sector of central angle $120^o$ of a circle is $3\pi\ cm^2$. Then, find the length of the corresponding arc of this sector.
- The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.
- A sector is cut-off from a circle of radius \( 21 \mathrm{~cm} \). The angle of the sector is \( 120^{\circ} \). Find the length of its arc and the area.
- 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 \( O A B \).
- Find the area of the sector of a circle of radius \( 5 \mathrm{~cm} \), if the corresponding arc length is \( 3.5 \mathrm{~cm} \).
- The perimeter of a sector of a circle of radius \( 5.7 \mathrm{~m} \) is \( 27.2 \mathrm{~m} \). Find the area of the sector.
- Find the area of sector of a circle of radius 5cm , if the corresponding arc length is 3.5cm.
- Figure below shows a sector of a circle of radius $r\ cm$ containing an angle $\theta^o$. The area of the sector is $A\ cm^2$ and perimeter of the sector is $50\ cm$. Prove that \( \theta=\frac{360}{\pi}\left(\frac{25}{r}-1\right) \)"\n
- Area of a sector of central angle \( 200^{\circ} \) of a circle is \( 770 \mathrm{~cm}^{2} \). Find the length of the corresponding arc of this sector.

Advertisements