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What will be the area of the sector whose central angle is $72 °$ , if the circumference of the circle is 88 cm?

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1.02 cm 2

1.04 cm 2

1.05 cm 2

1.03 cm 2

answer is A.

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Detailed Solution

We have to find the area of the sector whose central angle is

72 °

, if the circumference of the circle is 88 cm.
Suppose the radius of the circle is r.
Calculating the circumference,

⇒ 2 π r = 8 ⇒ r = 1411 cm

Area occupied by a sector of a circle having an angle

θ

= θ 360 × π r 2

where, r is the radius of the circle and

θ

is the sector angle.
Calculating the area of the sector,

= 72 ° 360 ° × 227 × 14112 = 1.02 cm 2

So, the area of the sector of the circle is

1.02 cm 2

Therefore, option 1 is correct.

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