Question

Area of a sector of a circle of radius 21 cm and the central angle 60° is:

• A. 211 cm²
• B. 221 cm²
• C. 231 cm²
• D. 241 cm²

Hint:

To calculate the area of a sector, use the formula \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Answer 1

The Correct Option is B

The area of a sector of a circle is given by the formula: \[ A = \frac{\theta}{360} \times \pi r^2 \] where \( \theta \) is the central angle and \( r \) is the radius of the circle. Here, \( \theta = 60^\circ \) and \( r = 21 \, \text{cm} \). Substitute the values into the formula: \[ A = \frac{60}{360} \times \pi \times (21)^2 \] \[ A = \frac{1}{6} \times \pi \times 441 \] \[ A = \frac{441 \pi}{6} \approx \frac{441 \times 3.1416}{6} \approx \frac{1385.44}{6} \approx 231 \, \text{cm}^2 \]
Step 2: Conclusion.
Therefore, the area of the sector is approximately \( 231 \, \text{cm}^2 \). Final Answer:} 231 cm².