Question

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.

Answer 1

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