Question

Find the angle subtended at the centre of a circle by an arc, for the following.
(i) radius of circle = 5.5m, length of arc = 6.05m ($\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Given:
Radius of the circle, r = 5.5 m
Length of the arc, l = 6.05 m
We have to find the angle subtended at the centre of the circle ($\mathrm{\theta }$).
Now,
Length of the arc, l = $\frac{\mathrm{\theta }}{360}\times 2\mathrm{\pi }r$

$\Rightarrow$6.05 = $\frac{\mathrm{\theta }}{360}\times 2\times \frac{22}{7}\times 5.5$

$$\begin{gathered} \Rightarrow \mathrm{\theta }=\frac{360\times 6.05\times 7}{22\times 2\times 5.5} \\ \Rightarrow \mathrm{\theta }=63° \end{gathered}$$

Thus, the arc subtends an angle of 63$°$ at the centre.