Calculate the perimeter of a sector of a circle of raduis 12cm and angle 60o.

1. Analyze the question

We are asked to find the perimeter of a sector of a circle.

• Radius ($r$): 12 cm
• Angle ($\theta$): 60°

2. Explain the concept

The perimeter of a sector is not just the length of the curved arc; it is the total distance around the shape. A sector is bounded by two radii and an arc.

• Formula for Arc Length ($L$): $L = \frac{\theta}{360} \times 2\pi r$
• Formula for Perimeter of a Sector: $P = \text{Arc Length} + 2r$ (because you must include the two straight radii).

3. Show the solution

Step 1: Calculate the Arc Length ($L$) Using the formula $L = \frac{\theta}{360} \times 2\pi r$: $L = \frac{60}{360} \times 2 \times \pi \times 12$ $L = \frac{1}{6} \times 24\pi$ $L = 4\pi \text{ cm}$

Step 2: Calculate the Perimeter ($P$) The perimeter includes the arc length plus the two radii that form the sides of the sector: $P = L + r + r$ $P = 4\pi + 12 + 12$ $P = 4\pi + 24$ $P = (24 + 4\pi) \text{ cm}$

4. Identify the answer

Comparing our result with the given options: A. (12 + 4$\pi$)cm B. (24 + 4$\pi$)cm C. (12 + 6$\pi$)cm D. (24 + 6$\pi$)cm

The calculated value matches option B.

5. Tip

A common mistake in JAMB exams is calculating only the arc length and forgetting to add the two radii. Always visualize the shape: a sector looks like a slice of pizza—to walk around the edge, you must walk along the crust (arc) and then back along both straight sides (radii).