Calculate the length of the arc of a circle of radius $31.0 \, cm$ which subtends an angle of $\frac{\pi}{6}$ at the centre.

(N/A) The formula for the plane angle $\theta$ in radians is given by $\theta = \frac{l}{r}$,where $l$ is the arc length and $r$ is the radius of the circle.
Given,$\theta = \frac{\pi}{6}$ radians and $r = 31.0 \, cm$.
Substituting these values into the formula:
$\frac{\pi}{6} = \frac{l}{31.0}$
Solving for $l$:
$l = 31.0 \times \frac{\pi}{6} \, cm$
Using $\pi \approx 3.14159$:
$l = 31.0 \times \frac{3.14159}{6} \, cm \approx 16.231 \, cm$.
Rounding to three significant figures (as the radius $31.0$ has three significant figures),the arc length is $16.2 \, cm$.