Question

Area of a sector of a circle with radius 4 cm and angle 30° is (use \( \pi = 3.14 \)):

• A. \( 4.08 \, \text{cm}^2 \)
• B. \( 4 \, \text{cm}^2 \)
• C. \( 4.18 \, \text{cm}^2 \)
• D. \( 41.8 \, \text{cm}^2 \)

Hint:

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

Answer 1

The Correct Option is A

Step 1: Formula for the Area of a Sector.
The area \( A \) 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. 
Step 2: Substituting the Given Values.
Here, the radius \( r = 4 \, \text{cm} \) and the angle \( \theta = 30^\circ \). Substituting these values into the formula, we get: \[ A = \frac{30}{360} \times 3.14 \times 4^2 \] \[ A = \frac{30}{360} \times 3.14 \times 16 = \frac{1}{12} \times 3.14 \times 16 \] \[ A = \frac{1}{12} \times 50.24 = 4.08 \, \text{cm}^2 \] 
Step 3: Conclusion.
Thus, the area of the sector is \( 4.08 \, \text{cm}^2 \).