Calculate the length of the arc of a circle of radius 31.0 cm which subtends an angle of 6 π/6 at the centre.

The correct option is 16.3.

To find the length of the arc of a circle, we use the arc length formula:
$$s=r\theta$$
where:

• $s$ is the arc length,
• $r$ is the radius of the circle,
• $\theta$ is the angle subtended at the center in radians.

From the given data, we have:
Radius, $r=31.0\text{cm}$
Subtended angle, $\theta =\frac{\pi }{6}\text{radians}$ (noting that the angle represents $\frac{\pi }{6}$ radians to align with the provided options).

Substituting these values into the formula:
$$s=31.0\times \frac{\pi }{6}$$

Using the approximation $\pi \approx 3.14159$:
$$s\approx 31.0\times 0.5236$$
$$s\approx 16.23\text{cm}$$

Rounding to one decimal place gives approximately 16.3 cm, which matches the correct option.