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Arcs have been drawn with radii $14$ cm each and with centres $P, Q, R$ . The area of the shaded region from the following choices is:

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224 cm 2

250 cm 2

308 cm 2

320 cm 2

answer is C.

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Detailed Solution

It is given that, the radius of the arc is

14

cm.

The area of the shaded region is the sum of the

3

sectors with different angles

θ 1, θ 2, θ 3

.
Area of the shaded region

= θ 1 π r 1 2 360 ° + θ 2 π r 2 2 360 ° + θ 3 π r 3 2 360 °

Since

r 1 = r 2 = r 3 = 14

,
Then the area of the shaded region is,

= π r 2 360 ° [θ 1 + θ 2 + θ 3]

The sum of the angles in a triangle is

180 °

= 227 × (14) 2 × 180 ° 360 ° = 22 × 14 = 308

The area of the shaded region is

308 cm 2

.
Hence option 3) is correct.

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