Question

Find the area of sector whose arc length and radius are 10 cm and 5 cm respectively.

Answer 1

Length of an arc subtending an angle $\theta =\frac{\theta }{360}\times 2\pi R$ where $R$ is the radius of the circle.
So, $10=\frac{\theta }{360}\times 2\times \frac{22}{7}\times 5$

$\theta ={114.45}^0$

Area of a sector of a circle of radius 'r' and angle $\theta =\frac{\theta }{360}\pi r^2$
Hence, area of the sector of the circle $=\frac{114.45}{360}\times \frac{22}{7}\times 5\times 5=25{cm}^2$