Answer
424.2k+ views
Hint: The sector is basically a portion of a circle which is enclosed by two radii and an arc. A sector divides the circle into two regions, namely major and minor sectors. The smaller area is known as the minor sector, whereas the region having a greater area is known as the major sector.
The area of a sector of the circle is calculated by using the formula:
Area =$\pi {r^2} \times \left( {\dfrac{\theta }{{360^\circ }}} \right)$, where ‘θ’ is the angle subtended at the centre.
Complete step by step solution:
Here, according to the question
Radius of the sector = 21 cm
Angle subtended by the arc at centre= θ = 120°
Now, we calculate the area of sector OAB
Area of the sector = $\pi {r^2}\dfrac{\theta }{{360}}$
$\begin{gathered}
= \dfrac{{22}}{7} \times 21 \times 21 \times \dfrac{{120}}{{360}} \\
= \dfrac{{22 \times 21 \times 21}}{{7 \times 3}} \\
= 462c{m^2} \\
\end{gathered} $
Therefore, the area of the sector is 462 $cm^2$
Note: If the length of the arc of the sector is given instead of the angle of the sector, then we will use the different method to calculate the area of the sector. Let the length of the arc be ‘l’. For the radius of a circle equal to r units, an arc of length r units will subtend 1 radian at the centre. Hence, it can be concluded that an arc of length ‘l’ will subtend$\dfrac{l}{r}$, the angle at the centre. So, if l is the length of the arc, r is the radius of the circle and θ is the angle subtended at the centre, then;
$\theta = \dfrac{l}{r}$, where θ is in radian. Therefore, the area of sector = $A = \dfrac{{\left( {lr} \right)}}{2}$
The area of a sector of the circle is calculated by using the formula:
Area =$\pi {r^2} \times \left( {\dfrac{\theta }{{360^\circ }}} \right)$, where ‘θ’ is the angle subtended at the centre.
Complete step by step solution:
Here, according to the question
Radius of the sector = 21 cm
Angle subtended by the arc at centre= θ = 120°
![seo images](https://www.vedantu.com/question-sets/18d7f9fc-79ed-4e33-911c-404ef41aa6e46576500009060210495.png)
Now, we calculate the area of sector OAB
Area of the sector = $\pi {r^2}\dfrac{\theta }{{360}}$
$\begin{gathered}
= \dfrac{{22}}{7} \times 21 \times 21 \times \dfrac{{120}}{{360}} \\
= \dfrac{{22 \times 21 \times 21}}{{7 \times 3}} \\
= 462c{m^2} \\
\end{gathered} $
Therefore, the area of the sector is 462 $cm^2$
Note: If the length of the arc of the sector is given instead of the angle of the sector, then we will use the different method to calculate the area of the sector. Let the length of the arc be ‘l’. For the radius of a circle equal to r units, an arc of length r units will subtend 1 radian at the centre. Hence, it can be concluded that an arc of length ‘l’ will subtend$\dfrac{l}{r}$, the angle at the centre. So, if l is the length of the arc, r is the radius of the circle and θ is the angle subtended at the centre, then;
$\theta = \dfrac{l}{r}$, where θ is in radian. Therefore, the area of sector = $A = \dfrac{{\left( {lr} \right)}}{2}$
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)