Question

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

Answer 1

Given:
Radius of the circle, r = 5 cm
Length of the arc, l = 10 cm
We will find the angle subtended at the centre of the circle, $\mathrm{\theta }$.
We know:
Length of the arc, l = $\frac{\mathrm{\theta }}{360}\times 2\mathrm{\pi }r$

⇒ 10 = $\frac{\mathrm{\theta }}{360}\times 2\times \frac{22}{7}\times 5$

$$\begin{gathered} \Rightarrow \mathrm{\theta }=\frac{360\times 10\times 7}{22\times 2\times 5} \\ \Rightarrow \mathrm{\theta }=114.5° \end{gathered}$$

Therefore, the arc subtends an angle of 114.5$°$ at the centre.
We know:
Area of a sector = $\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{r}^2$

Now,
Area of the sector = $\frac{114.5}{360}\times \frac{22}{7}\times 5^2$

= $\frac{62975}{2520}$
= 24.99
$\approx$25 cm²
Thus, the area of the sector is 25 cm².