Question

The length of an arc of a circle, subtending an angle of 54° at the centre, is 16.5 cm. Calculate the radius, circumference and area of the circle.

Answer 1

Length of the arc = 16.5 cm
$\theta ={54}^{\circ }$
Radius = ?
Circumference=?
We know:
Length of the arc $=\frac{2\mathrm{\pi r\theta }}{360}$
$$\begin{gathered} \Rightarrow 16.5=\frac{2\times {\displaystyle \frac{22}{7}}\times r\times 54}{360} \\ \Rightarrow r=\frac{16.5\times 360\times 7}{44\times 54} \\ \Rightarrow r=17.5\mathrm{cm} \end{gathered}$$

$$\begin{gathered} c=2\mathrm{\pi r} \\ =2\times \frac{22}{7}\times 17.5 \\ =110\mathrm{cm} \end{gathered}$$

Circumference = 110 cm

Now,
Area of the circle =${\mathrm{\pi r}}^2$
$$\begin{gathered} =\frac{22}{7}\times 17.5\times 17.5 \\ =962.5{\mathrm{cm}}^2 \end{gathered}$$