Question

Find the area of a sector of a circle with radius $14cm$, if the length of the corresponding arc is $22cm$.

Answer 1

We have,

Radius of circle$=14cm.$

Length of arc$=22cm.$

Using formula,

$Angle=\frac{radius}{arc}$

Now,

$Angle=\frac{22}{14}$

$Angle=\frac{22}{2\times 7}$

$Angle=\frac{\pi }{2}(\pi =\frac{22}{7})$

$Angle=\theta =\frac{\pi }{2}$

So,

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

$=\frac{{90}^o}{{360}^o}\times \frac{22}{7}\times 14\times 14$

$=\frac{1}{4}\times 22\times 2\times 14$

$=22\times 7$

$=154sq.cm.$

Hence, this is the answer.