Question

If the sector of a circle has an angle 60° at the centre and its area 20cm^2 then find the area of same circle.

Answer 1

Step-by-step explanation:

$area \: of \: sector = \frac{\pi \times radius {}^{2} }{6} = 20cm {}^{2} \\ radius {}^{2} = \frac{120}{\pi} \\ radius = \sqrt{ \frac{120}{\pi} } = 6.18cm \\ area \: of \: circle = \pi \times radius {}^{2} = \pi \times 6.18 \times 6.18 \\ = 119.98 \: cm {}^{2}$

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Answer 2

$\huge{\bold{ <u>Given</u><u> </u>:- }}$

Angle of sector = 60°

Area of sector = 20 sq.cm

$\huge{\bold{<u>To</u><u> </u>find :-}}$

The area of same circle ..

$\huge{\bold{Solution:-}}$

We know that ,

$Area \: of \: sector \: = \frac{ \theta}{360} \times \pi \: {r}^{2} \\ \\ \rightarrow 20 \: = \frac{60}{360} \times \pi \: {r}^{2} \\ \\ \rightarrow \: 20 = \frac{1}{6} \times \pi \: {r}^{2} \\ \\ \rightarrow20 \times 6 = \pi \: {r}^{2} \\ \\ \rightarrow\pi \: {r}^{2} = 120 \\ \\Hence ,\\ {\purple{\boxed{\large{\bold{The \: area \: of \: same \: circle = 120 \: sq.cm}}}}}$

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