The area of the circle is $25\pi$ sq. cms. Find the length of its arc subtending an angle of $144^o$ at the centre. Also find the area of the corresponding sector.

Area of circle = $\pi r^2$
$25\pi =\pi r^2⟹r=5$

Arc-length = $\pi \frac{\theta }{180^o}r$

                   =$\pi \frac{144^o}{180^o}\cdot 5$

                   =$\pi \frac{4}{5}\cdot 5$

                   =$4\pi$ cm

Area of sector = $\pi \frac{\theta }{360^o}{r}^2$

                         =  $\pi \frac{144}{360^o}\cdot 25$

                         =  $\pi \frac{2}{5}\cdot 25$

                         =  $10\pi$ sq.cm