Question

The area of a sector of a circle of $6cm$ radius is $15\pi sq.cm$. Find the measure of are and length of the arc corresponding to the sector.

Answer 1

Area of sector $=15\pi c{m}^2$

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

Hence,

$15\pi =\frac{\theta }{36}\times \pi \times 6\times 6$

$\Rightarrow \theta =150$

Length of are $=\frac{\theta }{360}\times 2\pi r$

$=\frac{150}{360}\times 2\times \pi \times 6$

$=5\pi cm$