An arc subtends an angle of 30º at the centre of a circle radius 12cm. Calculate the length of the arc.

Analysis

The question asks for the length of an arc of a circle. To find this, we need the radius of the circle and the angle subtended by the arc at the center.

Concept

The length of an arc ($L$) is a portion of the circumference of a circle. The formula is derived from the ratio of the central angle ($\theta$) to the total angle in a circle ($360^\circ$):

Where:

• $\theta$ = angle subtended at the center
• $r$ = radius of the circle
• $\pi$ = a constant (usually left as $\pi$ in JAMB questions unless specified otherwise)

Step-by-Step Solution

1. Identify the given values: • $\theta = 30^\circ$ • $r = 12\text{ cm}$

2. Substitute the values into the formula: $$L = \frac{30}{360} \times 2 \times \pi \times 12$$

3. Simplify the fraction: $$\frac{30}{360} = \frac{3}{36} = \frac{1}{12}$$

4. Calculate the final length: $$L = \frac{1}{12} \times 2 \times \pi \times 12$$

Notice that the $12$ in the numerator and the $12$ in the denominator cancel each other out:

Conclusion

Comparing our result to the options provided, the calculated length is $2\pi\text{ cm}$. This matches option B.

Exam Tip: In JAMB Mathematics, always look at the options before calculating. Since the options are expressed in terms of $\pi$, do not substitute $3.142$ or $22/7$ for $\pi$. Keeping $\pi$ as a symbol saves time and prevents unnecessary decimal errors!