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Area of a sector of central angle $200 °$ of a circle is $770 cm 2$ . From the following choices, the length of the corresponding arc of this sector is:

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15613 cm

713 cm

7313 cm

2213 cm

answer is C.

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Detailed Solution

It is given that, area of a sector of central angle

200 °

of a circle is

770 cm 2

Obtain the radius of the sector.
Let the radius be

r

.
Area of the sector

= θ 360 ° × π r 2

770 = 200 ° 360 ° × π (r) 2

r = 770 × 95 × 722

= 21 cm

Obtain the length of the sector by using the formula,
= Central angle

×

Radius

= θ × r = 200 ° × 21

Since

1 ° = π 180 ° r a d i a n s

l e n g t h = 200 ° × 21 × 227 180 °

= 2203 = 7313

The length is

7313 c m

.
Hence, option 3) is correct.

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