Q.OPQ is the sector of a circle having centre at O and radius 15 cm. If $m\angle POQ = 30°$, find the area enclosed by arc PQ and chord PQ.

Step 1: $\theta = 30°\times\frac{\pi}{180}=\frac{\pi}{6}$ radian, $r=15$ cm.

Step 2: Sector area $=\frac12 r^2\theta = \frac12(225)\left(\frac{\pi}{6}\right)=\frac{225\pi}{12}=\frac{75\pi}{4}$ sq.cm.

Step 3: Triangle area $=\frac12 r^2\sin\theta = \frac12(225)\sin30° = \frac12(225)(0.5)=56.25=\frac{225}{4}$ sq.cm. …

Subtract the triangle area (½r²sinθ) from the sector area (½r²θ) to …

• Forgetting to convert 30° to radian for the sector-area part while correctly using sin30° for the triangle.
• Arithmetic slip combining the two fractions with denominator 4. …