Question

Find the area of sector whose angle is 120°and radius is 21cm

Answer 1

Answer:

Given :-

• A circle whose angle is 120° and the radius is 21 cm.

To Find :-

• What is the area of sector.

Formula Used :-

$\clubsuit$ Area Of Sector Formula :

$\mapsto \sf\boxed{\bold{\pink{Area_{(Sector)} =\: \dfrac{\theta}{360^{\circ}} \times {\pi}r^2}}}$

where,

• $\sf \theta$ = Central Angle of a Circle
• $\sf \pi$ = pie or 22/7
• r = Radius of a Circle

Solution :-

Given :

• Central Angle of Circle ($\sf \theta$) = 120°
• Radius (r) = 21 cm

According to the question by using the formula we get,

$\longrightarrow \sf Area_{(Sector)} =\: \dfrac{120^{\circ}}{360^{\circ}} \times \dfrac{22}{7} \times (21)^2$

$\longrightarrow \sf Area_{(Sector)} =\: \dfrac{120^{\circ}}{360^{\circ}} \times \dfrac{22}{7} \times 21 \times 21$

$\longrightarrow \sf Area_{(Sector)} =\: \dfrac{120^{\circ}}{360^{\circ}} \times \dfrac{22}{\cancel{7}} \times {\cancel{441}}$

$\longrightarrow \sf Area_{(Sector)} =\: \dfrac{12\cancel{0^{\circ}}}{36\cancel{0^{\circ}}} \times 1386$

$\longrightarrow \sf Area_{(Sector)} =\: \dfrac{12}{36} \times 1386$

$\longrightarrow \sf Area_{(Sector)} =\: \dfrac{\cancel{16632}}{\cancel{36}}$

$\longrightarrow \sf\bold{\red{Area_{(Sector)} =\: 462\: cm^2}}$

${\small{\bold{\underline{\therefore\: The\: area\: of\: sector\: is\: 462\: cm^2\: .}}}}$

Answer 2

$\ \qquad { \dag \cal{Q} \frak{uestion}}$

$\sf\: Find \: the \: area \: of \: sector \: whose \: angle \: is \: 120° \: and \: radius \: is \: 21cm.$

$\:$

$\ \qquad \dag \frak{Solution}$

$\sf→Area \: of \: sector= \frac{0}{360} \times \pi \times {r}^{2}$

$\sf→Area \: of \: sector= \frac{120}{360} \times \frac{22}{7} \times 21 \times 21$

$\sf→Area \: of \: sector= \red{462 {cm}^{2} }$

$\:$

$\bold \red{Celestial} \bold{Centrix}$