Q.The area of a circle is $25\pi$ sq.cm. Find the length of its arc subtending an angle of $144°$ at the centre. Also find the area of the corresponding sector.

Step 1: $\pi r^2 = 25\pi \Rightarrow r^2=25 \Rightarrow r=5$ cm.

Step 2: $\theta = 144°\times\frac{\pi}{180}=\frac{4\pi}{5}$ radian.

Step 3: Arc length $s=r\theta = 5\times\frac{4\pi}{5}=4\pi$ cm. …

Find r from πr² = given circle area, convert the angle to radian, t …

• Confusing the CIRCLE's area (25π) with the SECTOR's area when solving for r. …