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What will be the area of the major segment APB of a circle of radius 35 cm and $∠ A O B = 90 °$ ?

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5300 cm 2

3500 cm 2

3510 cm 2

3505 cm 2

answer is B.

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Detailed Solution

We have to find the area of the major segment APB of a circle of radius 35 cm and

∠ A O B = 90 °

Calculating the area of the minor segment,

Area of segment= θ 3600 × π r 2

Area of minor segment = Area of sector AOBC − Area of right triangle AOB

= 90 ° 360 ° × π (O A) 2 − 12 × O A × O B = 14 × 227 × (35) 2 − 12 × 35 × 35 = 962.5 − 612.5 = 350 cm 2

Calculating the area of the major segment,
Area of major segment APB = Area of the circle − area of the minor segment

= π (O A) 2 − 350 = 227 × (35) 2 − 350 = 3850 − 350 = 3500 cm 2

So, the area of major segment is

3500 cm 2

.
Therefore, option 2 is correct.

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