# In figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region. - Mathematics

Sum

In figure, arcs have been drawn with radii 14 cm each and with centres P, Q and R. Find the area of the shaded region.

#### Solution

Given that, radii of each arc (r) = 14 cm

Now, area of the sector with central ∠P = (∠P)/360^circ xx pir^2

= (∠P)/360^circ xx pi xx (14)^2 cm   ......[∵ Area of any sector with central angle θ and radius r = (pir^2)/360^circ xx theta]

Area of the sector with central angle = (∠Q)/360^circ xx pir^2 = (∠Q)/360^circ xx pi xx (14)^2  cm^2

And area of the sector with central-angle R = (∠R)/360^circ xx pir^2 xx (∠R)/360^circ xx  pi xx (14)^2  cm^2

Therefore, sum of the areas (in cm2) of three sectors

= (∠P)/360^circ xx pi xx (14)^2 + (∠theta)/360^circ xx pi xx (14)^2 + (∠R)/360^circ xx pi xx (14)^2

= (∠P + ∠Q + ∠R)/360^circ xx 196 xx pi

= 180^circ/360^circ xx 196 pi  cm^2  .....[Since, sum of all interior angles in any triangle is 180°]

= 98 pi  cm^2 = 98 xx 22/7

= 14 xx 22

= 308 cm2

Hence, the required area of the shaded region is 308 cm2.

Concept: Areas of Sector and Segment of a Circle
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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.3 | Q 13 | Page 128
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