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 $=\frac{2\mathrm{\pi r\theta }}{360}$

$$\begin{gathered} \Rightarrow 44=2\times \frac{22}{7}\times 17.5\times \frac{\theta }{360} \\ \Rightarrow \theta =\frac{44\times 7\times 360}{44\times 17.5} \\ \Rightarrow \theta ={144}^{\circ } \end{gathered}$$
Also,
Area of the sector =$\frac{{\mathrm{\pi r}}^2\mathrm{\theta }}{360}$

$$\begin{gathered} =\frac{22}{7}\times 17.5\times 17.5\times 144 \\ =385{\mathrm{cm}}^2 \end{gathered}$$