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In the Given Figure, If O is the Center of the Circle, Pq is a Chord. ∠ Poq = 90°, Area of the Shaded Region is 114 Cm2, Find the Radius of the Circle. π = 3.14) - Geometry

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Sum

In the given figure, if O is the center of the circle, PQ is a chord. \[\angle\] POQ = 90°, area of the shaded region is 114 cm2, find the radius of the circle. \[\pi\] = 3.14)

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Solution

∠POQ = θ = 90º
Let the radius of the circle be r cm.
Area of the shaded region = Area of the segment PRQ = 114 cm

\[\therefore r^2 \left( \frac{\pi\theta}{360° } - \frac{\sin\theta}{2} \right) = 114\]

\[ \Rightarrow r^2 \left( \frac{3 . 14 \times 90° }{360°  } - \frac{\sin90° }{2} \right) = 114\]

\[ \Rightarrow r^2 \left( \frac{3 . 14}{4} - \frac{1}{2} \right) = 114\]

\[ \Rightarrow r^2 \times \left( 0 . 785 - 0 . 5 \right) = 114\]

\[ \Rightarrow r = \sqrt{\frac{114}{0 . 285}}\]

\[ \Rightarrow r = \sqrt{400} = 20 cm\]

Thus, the radius of the circle is 20 cm.

Concept: Areas of Sector and Segment of a Circle
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Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 7 Mensuration
Practice set 7.4 | Q 4 | Page 160
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