Question

The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44 cm in length.

Answer 1

Given:

Radius = 17.5 cm

Length of the arc = 44 cm

Now,

Length of the arc${\displaystyle =\frac{2\pi \text{r}\theta }{360}}$

${\displaystyle \Rightarrow 44=2\times \frac{22}{7}\times 17.5\times \frac{\theta }{360}}$

${\displaystyle \Rightarrow \theta =\frac{44\times 7\times 360}{44\times 17.5}}$

⇒ θ = 144

Also,

Area of the sector ${\displaystyle =\frac{\pi {\text{r}}^2\theta }{360}}$

${\displaystyle =\frac{22}{7}\times 17.5\times 17.5\times 144}$

= 385 cm²