Question

A sector of angle 80° is cut-out from a circle. If the arc length is 26.4 cm. Find the area of
the sector.
​

Answer 1

Given that ,

Angle of sector = 80°

Length of arc of sector = 26.4 cm

We know that , the length of arc of sector is given by

$\sf\large\fbox{Length \: of \: arc = \frac{ \theta}{360} \times 2\pi r}$

Thus ,

$\sf \mapsto26.4 = \frac{80 \times 2 \times 22 \times r}{360 \times 7} \\ \\ \sf \mapsto26 .6 = \frac{8 \times 11 \times r}{9 \times 7} \\ \\ \sf \mapsto26.4 = \frac{88 \times r}{9 \times 7} \\ \\ \sf \mapsto1663.2 = 88 \times r \\ \\ \sf \mapsto = \frac{1663.2}{88} \\ \\ \sf \mapsto r = 18.9 \: \: m$

$\sf \therefore \underline{The \: radius \: of \: circle \: is \: 18.9 \: c m}$

Now , the area of sector is given by

$\sf \large\fbox{Area = \frac{ \theta}{360} \times \pi {r}^{2} }$

Thus ,

$\sf \mapsto Area = \frac{80 \times 22 \times {(18.9)}^{2} }{360 \times 7} \\ \\\sf \mapsto Area = \frac{4 \times 11 \times 27 \times 21}{ {(10)}^{2} } \\ \\\sf \mapsto Area = 24948 \times {(10)}^{ - 2} \\ \\\sf \mapsto Area = 249.48 \: \: {cm}^{2}$

$\therefore\sf \underline{The \: area \: of \: sector \: is \: 249.48 \: {cm}^{2} }$