An arc subtends an angle of 30o at the centre o... - JAMB Mathematics 2024 Question

The length of an arc can be calculated using the formula:

\(L = \frac{\theta}{360} \times 2\pi r\)

where:

• \(\theta\) is the angle subtended by the arc at the center of the circle (in degrees).
• \(r\) is the radius of the circle.

Step 1: Substitute the given values into the formula

Given:

• \(\theta = 30^\circ\)
• \(r = 12 \, \text{cm}\)

\(L = \frac{30}{360} \times 2\pi \times 12\)

Step 2: Simplify the fraction

\(\frac{30}{360} = \frac{1}{12}\)

So:

\(L = \frac{1}{12} \times 2\pi \times 12\)

Step 3: Simplify further

\(L = 2\pi \, \text{cm}\)