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Q.

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Then, the area of the shaded region will be ____ sq. cm.

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Detailed Solution

In the given figure, APB and CQD are semicircles of diameter 7 cm each, while ARC an BSD are semicircles of diameter 14 cm each. Then, the area of the shaded region will be 115.5 sq. cm.
Calculating the area of the shaded region,
Area of the arc

= 12 × π r 2

Area of shaded region = (Area of the arc APB) + (Area of the arc ARC)+ (Area of the arc BSD) + (Area of the arc CQD)
Suppose r1,r2,r3,r4 are the radius of arcs APB, ARC, BSD and CQD respectively.
Question Image

Question Image

Solving further,

= π 49 − 494 = 227 × 1474 = 115.5 cm 2

So, the area of the shaded region is

115.5 cm 2

.
Therefore, 115.5 is the correct answer.

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