Question

The area of the sector of a circle whose angle is \(60^\circ\) and radius \(12 \, \text{cm}\) will be

• A. \(18\pi \, \text{cm}^2\)
• B. \(20\pi \, \text{cm}^2\)
• C. \(24\pi \, \text{cm}^2\)
• D. \(30\pi \, \text{cm}^2\)

Hint:

The area of a sector depends directly on the central angle. For a full circle (\(360^\circ\)), the area is \(\pi r^2\).

Answer 1

The Correct Option is C

Step 1: Formula for the area of a sector.
\[ \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2 \]
Step 2: Substitute given values.
\[ \theta = 60^\circ, \quad r = 12 \, \text{cm} \] \[ \text{Area} = \frac{60}{360} \times \pi \times (12)^2 = \frac{1}{6} \times \pi \times 144 = 24\pi \]
Step 3: Conclusion.
Hence, the area of the sector is \(24\pi \, \text{cm}^2\).