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Solution


Q.

In the given figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Then:

(i) We need ∠P, ∠Q and ∠R to find combined area of shaded region
(ii) Area of shaded region 308 cm²

(iii) Angles are needed to find area of respective sector.
(iv) Arc length at P, Q, R = radius × respective angles in radian

Which of the above statements are correct. Choose the correct option from the following
1 (i), (ii) and (iv)  
2 (ii), (iii) and (iv)
 
3 (ii) and (iv)
 
4 (i), (ii) and (iv)  

Ans.

(2)

Area of sector =θ360×area of circleArea of sector at P = ∠P360×πr2Area of sector at Q = ∠Q360×πr2Area of sector at R =∠R360×πr2Total area of shaded region =∠P+∠Q+∠R360×πr2We know (Sum of interior angles of triangle) Area of shaded region=180360πr2=12πr2=12×227×14×14=308 cm2∴ (ii) is correct.Hence, we don’t need angles to find area of shaded region, so (i) is incorrect.Arc length = Radius × Angle in radians ∴ (iv) is correct.But we need angles to find respective arc length and areas of respective sectors. ∴ (iii) is correctHence (ii), (iii) and (iv) are correct.