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If the radii of the two concentric circles with centre O are 7 cm and 14 cm, respectively, and AOC = 40°, calculate the area of the shaded region in the given image.

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1533 c m 2

1543 c m 2

1553 c m 2

1563 c m 2

answer is B.

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Detailed Solution

Given that the radii of the two concentric circles with centre O are 7 cm and 14 cm, respectively.
Question Image

Radius of the small circle is 7 cm.
Radius of the big circle is 14 cm.
∠AOC=40°.
Area of shaded region = Area of sector AOC– Area of sector BOD
Area of sector AOC

= θ 360 × π r 2

where r is the radius of the circle.

⇒ A r e a = 40360 × 227 × 142 ⇒ A r e a = 19 × 22 × 2 × 14 ⇒ A r e a = 6169 c m 2

Area of sector BOD

= θ 360 × π r 2

⇒ A r e a = 40360 × 227 × 72 ⇒ A r e a = 19 × 22 × 7 ⇒ A r e a = 1549 c m 2

Area of the shaded region = Area of sector AOC– Area of sector BOD

⇒ A r e a = 6169 − 1549 ⇒ A r e a = 4629 ⇒ A r e a = 1543 c m 2

The area of the shaded region is

1543 c m 2

.
Therefore the answer is option (2).

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