Question

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.​

Answer 1

Step-by-step explanation:

$\mathfrak{ \huge{ \green{ \underline{given}}}} \\ \mathfrak{ \large{ \red{radius \: = \: 6 \: cm}}} \\ \mathfrak{ \large{ \red{angle \: of \: sector \: (θ) = {60}^{o}}}} \\ \mathfrak{ \huge{ \green{ \underline{to \: find}}}} \\ \mathfrak{ \large{ \red{area \: of \: sector \: = \: ?}}} \\ \mathfrak{ \huge{ \green{ \underline{formula \: to \: be \: used}}}} \\ \mathfrak{ \large{ \red{area \: of \: sector \: = \: \frac{θ}{360} \: \times \: \pi {r}^{2} }}} \\ \mathfrak{ \huge{ \green{ \underline{solution}}}} \\ \mathfrak{ \large{ \blue{area \: of \: sector \: = \frac{θ}{360} \times \pi {r}^{2}}}} \\ \mathfrak{ \large{ \blue{area \: of \: sector \: = \: \frac{60}{360} \times \frac{22}{7} \times 6 \times 6 }}} \\ \mathfrak{ \large{ \blue{area \: of \: sector \: = \: \frac{1}{6} \times \frac{22}{7} \times 6 \times 6 }}} \\ \mathfrak{ \large{ \blue{area \: of \: sector \: = \: \frac{22}{7} \times 6}}} \\ \mathfrak{ \large{ \orange{ \underline{area \: of \: sector \: = \: \frac{132}{7} {cm}^{2} }}}}$

Answer 2

${\huge {\underline {\bf {\blue {Question}}}}}$

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

${\huge {\underline {\bf {\blue {Answer}}}}}$

Given :-

• Radius of circle = 6 cm.
• Angle of the sector = 60°

To Find :-

• The area of a sector of a circle.

Solution :-

By using formula,

${\boxed {\sf {Area~ of~ sector = {\dfrac { \theta}{360°}} \pi {r}^{2} }}}$

$\implies$ ${\sf {Area~ of~ sector~ = {\dfrac {60°}{360°}} \times {\dfrac {22}{7}} \times {6}^{2} }}$

$~$

$\implies$ ${\sf {Area~ of~ sector~ = {\dfrac {{\cancel {60}}}{{\cancel {{360}}^{6}}}} \times {\dfrac {22}{7}} \times 36 }}$

$~$

$\implies$ ${\sf {Area~ of~ sector~ = {\dfrac {1}{ {\cancel {6}}}} \times {\dfrac {22}{7}} \times {\cancel {{36}}^{6}} }}$

$~$

$\implies$ ${\sf {Area~ of~ sector~ = {\dfrac {22 \times 6}{7}}}}$

$~$

$\implies$ ${\sf {Area~ of~ sector~ = {\dfrac {132}{7}}}}$

$~$

${\underline {\boxed {\sf {Area~ of~ sector~ = 18.85~ {cm}^{2}}}}}$

${\underline {\sf {\purple {Hence,~ area~ of~ the~ sector~ is~ 18.85~ {cm}^{2}}}}}$