Answer
Verified
396k+ 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°
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
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The cell wall of prokaryotes are made up of a Cellulose class 9 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
a Tabulate the differences in the characteristics of class 12 chemistry CBSE