#### Question

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)

#### 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 cm^{2}.

Is there an error in this question or solution?

Solution 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) Concept: Areas of Sector and Segment of a Circle.