Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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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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Question

A chord PQ of a circle with a radius of cm subtends an angle of 60° with the center of the circle. Find the area of the minor as well as the major segment. ( \[\pi\] = 3.14,  \[\sqrt{3}\] = 1.73)

Solution

The radius of the circle, r = 15 cm
Let O be the center and PQ be the chord of the circle. 

 

∠POQ = θ = 60º
Area of the minor segment = Area of the shaded region

\[= r^2 \left( \frac{\pi\theta}{360°} - \frac{\sin\theta}{2} \right)\]
\[ = \left( 15 \right)^2 \times \left( \frac{3 . 14 \times 60° }{360° } - \frac{\sin60° }{2} \right)\]
\[ = 225 \times \frac{3 . 14}{6} - 225 \times \frac{\sqrt{3}}{4}\]
\[ = 117 . 75 - 97 . 31\]
\[ = 20 . 44 {cm}^2\]

Now,
Area of the circle = 

\[\pi r^2 = 3 . 14 \times \left( 15 \right)^2 = 3 . 14 \times 225\]  = 706.5 cm2
∴ Area of the major segment = Area of the circle − Area of the minor segment = 706.5 − 20.44 = 686.06 cm2
Thus, the areas of the minor segment and major segment are 20.44 cm2 and 686.06 cm2, respectively.
  Is there an error in this question or solution?
Solution 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) Concept: Areas of Sector and Segment of a Circle.
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