Question

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

Answer 1

Given that:

Radius of the circle(r) = 6 cm

Angle of the sector (θ) = 60°

$area \: of \: the \: sector \: = \frac{θ}{360} \pi {r}^{2} \\ = \frac{60°}{360°} \times \frac{22}{7} \ \times {6}^{2} \\ \\ = \frac{1}{6} \times \frac{22}{7} \times 36 \\ \\ = \frac{22 \times 6}{7} \\ \\ = \frac{132}{7} \\ \\ = 18.714 {cm}^{2}$

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Answer 2

Step-by-step explanation:

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