Question

Find the area of the sector with a radius of 20 cm and an arc length of 88
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Answer 1

Given:-

radius of the circle = 20cm

length of the arc = 88cm

Formula used:-

$area \: of \: sector = \frac{theta}{360} \times \pi {r}^{2}$

$length \: of \: arc = \frac{theta}{360} \times 2\pi \times r$

Solution:-

We have,

r = 20cm

l = 88cm

$= > \frac{theta}{360} \times 2\pi \: r = 88 \\ = > \frac{theta}{360} \times 2 \times \frac{22}{7} \times 20 = 88$

let theta be x

$\frac{x}{360} \times \frac{44}{7} \times 2 = 88 \\ = > x = 88 \times \frac{7}{44} \times \frac{1}{20} \times 360 \\ = > x = \frac{7 \times 2}{20} \times 360 \\ = >x = 36\times 7$

therefore, x = 252

Now,

$area \: of \: sector = \frac{252}{360} \times \frac{22}{7} \times {20}^{2} \\ = \frac{0.7 \times 22}{7} \times 400 \\ = \frac{22}{10} \times 400 = 880 {cm}^{2}$

Hence, area of the required sector = 880cm^2