Question

Find the length of an arc of a circle of radius $14$ cm which subtends an angle of $30^\circ$ at the centre.

Hint:

The arc length formula is a direct proportion: arc length $=\dfrac{\text{angle}}{360^\circ}\times$ circumference.

Answer 1

Step 1: Use arc length formula.
Length of arc is given by \[ l=\frac{\theta}{360^\circ}\times 2\pi r. \]

Step 2: Substitute values.
Here, $r=14$ cm and $\theta=30^\circ$, so \[ l=\frac{30}{360}\times 2\pi \times 14 =\frac{1}{12}\times 28\pi =\frac{28\pi}{12} =\frac{7\pi}{3}. \]

Step 3: Simplify and approximate.
\[ l=\frac{7\pi}{3}\ \text{cm}. \] Using $\pi\approx 3.14$, \[ l=\frac{7\times 3.14}{3}=7.33\ \text{cm (approx)}. \] \boxed{\text{Arc length }=\frac{7\pi}{3}\ \text{cm } \approx 7.33\ \text{cm}}