Question

How do you find the length of arc subtended by a central angle of $30°$ in a circle of radius $10cm?$

Answer 1

Find the length of arc subtended by a central angle of $30°$ in a circle of radius $10cm$:

Let $\theta$ be angle subtended at the center of circle and $r$ be the radius of the given circle:

$\theta =30°,r=10cm$

Use the formula below to calculate the length of arc:

$\mathit{l}\mathbf{=}\frac{\mathbf{\theta }}{\mathbf{360}\mathbf{°}}\mathbf{\times }\mathbf{2}\mathbf{\pi r}$

($l$ is the length of arc)

Substitute $30°\text{for}\theta and10\text{for}r$:

$\begin{array}{rcl}l& =& \frac{30}{360}\times 2\times \frac{22}{7}\times 10\\ & \Rightarrow & =\frac{110}{21}\\ & \approx & 5.24\end{array}$

Hence, the length of arc subtended is $\mathbf{5}\mathbf{.}\mathbf{24}\mathbf{}\mathit{c}\mathit{m}$ approximately.