The length of an arc of a circle, subtending an angle of 54° at the centre, is 16.5 cm.
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.

Solution:

Length of the arc = 16.5 cm

$\theta=54^{\circ}$

Circumference=?
We know:

Length of the $\operatorname{arc}=\frac{2 \pi \mathrm{r} \theta}{360}$

$\Rightarrow 16.5=\frac{2 \times \frac{22}{7} \times r \times 54}{360}$

$\Rightarrow r=\frac{16.5 \times 360 \times 7}{44 \times 54}$

$\Rightarrow r=17.5 \mathrm{~cm}$

$c=2 \pi \mathrm{r}$

$=2 \times \frac{22}{7} \times 17.5$

$=110 \mathrm{~cm}$

Circumference = 110 cm

Now,

Area of the circle $=\pi r^{2}$

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

$=962.5 \mathrm{~cm}^{2}$