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प्रश्न
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.
उत्तर
Given that, radii of each arc (r) = 14 cm
Now, area of the sector with central angle P
= `(∠"P")/360^circ xx π"r"^2`
= `(∠"P")/360^circ xx π xx (14)^2 "cm"^2`
Area of the sector with central angle Q
= `(∠"Q")/360^circ xx π"r"^2`
= `(∠"Q")/360^circ xx π xx (14)^2 "cm"^2`
And area of the sector with central angle R
= `(∠"R")/360^circ xx π"r"^2`
= `(∠"R")/360^circ xx π xx (14)^2 "cm"^2`
Therefore, sum of the areas of three sectors
= `(∠"P")/360^circ xx π xx (14)^2 + (∠"Q")/360^circ xx π xx (14)^2 + (∠"R")/360^circ xx π xx (14)^2`
= `π/360^circ xx (14)^2 xx [∠"P" + ∠"Q" + ∠"R"]`
= `π/360^circ xx 196 xx 180^circ` ...[Since, sum of all interior angles in any triangle is 180°]
= 98π
= `98 xx 22/7`
= 14 × 22
= 308
Hence, the required area of the shaded region is 308 cm2.
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