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In the Given Figure, If a is the Centre of the Circle. ∠ Par = 30°, Ap = 7.5, Find the Area of the Segment Pqr ( π = 3.14) - Geometry

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Sum

In the given figure, if A is the centre of the circle. \[\angle\] PAR = 30°, AP = 7.5, find the area of the segment PQR ( \[\pi\]  = 3.14)

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Solution

Radius of the circle, r = 7.5 cm
∠​PAR = θ = 30º 
∴ Area of segment PQR

\[= r^2 \left( \frac{\pi\theta}{360°} - \frac{\sin\theta}{2} \right)\]
\[ = \left( 7 . 5 \right)^2 \left( \frac{3 . 14 \times 30° }{360° } - \frac{\sin30° }{2} \right)\]
\[ = 56 . 25 \times \left( \frac{3 . 14}{12} - \frac{1}{4} \right)\]
\[ = 56 . 25 \times 0 . 01167\]
\[ = 0 . 65625 {cm}^2\]

Thus, the area of the segment PQR is 0.65625 cm2.

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

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 7 Mensuration
Practice set 7.4 | Q 3 | Page 160
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