Question

The circumference of a circle is 220 cm. An arc of the circle subtends 60% at the centre of it. Then find the area of the corresponding major sector?
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Answer 1

Answer:

your solution is as follows

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Step-by-step explanation:

$to \: find : \\ area \: of \: major \: corresponding \: sector \\ \\ given \: that : \\ circumference \: of \: circle = 220.cm \\ central \: angle \: (θ) = 60 \: \\ \\ we \: know \: that \\ circumference \: of \: any \: circle = 2\pi.r \\ 2\pi.r = 220 \\ \\ 2 \times \frac{22}{7} \times r = 220 \\ \\ \frac{2}{7} \times r = 10 \\ \\ \frac{r}{7} = 5 \\ \\ r = 35.cm$

$thus \: then \: \\ area \: of \: circle = \pi.r {}^{2} \\ \\ = \frac{22}{7} \times 35 \times 35 \\ \\ = 22 \times 5 \times 35 \\ \\ = 110 \times 35 \\ \\ = 3850 \: cm {}^{2} \\ \\ so \: then \: \\ area \: of \: major \: sector = \pi.r {}^{2} - \frac{θ}{360} \times \pi.r {}^{2} \\ \\ = \pi.r {}^{2} (1 - \frac{θ}{360} \: ) \\ \\ = 3850 \times (1 - \frac{60}{360} ) \\ \\ = 3850 \times (1 - \frac{1}{6} ) \\ \\ = \frac{3850 \times 5}{6} \\ \\ = \frac{19250}{6} \: cm {}^{2}$