Question

The length of an arc of a circle, subtending an angle of ${54}^{\circ }$ at the center is $16.5\text{cm}$. Calculate the radius, circumference and area of the circle.

Answer 1

Given:

Length of the arc $=16.5\text{cm}$

$\theta =54°$

To find:

Radius $=?$

Cicumference $=?$

Area of the circle $=?$

Length of arc $=\frac{\theta }{360°}\times 2\pi r$

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

$\Rightarrow r=\frac{16.5\times 20\times 7}{3\times 22\times 2}$

$\Rightarrow r=17.5\text{cm}$

Now,

$\text{Circumference}=2\pi r=2\times \frac{22}{7}\times 17.5=110\text{cm}$

Also,

Area of circle

$=\pi r^2=\frac{22}{7}\times {\left(17.5\right)}^2=22\times 2.5\times 17.5=962.5{\text{cm}}^2$