Question

The area of a sector, whose radius is 7 cm with the angle 72° is:

• A. 38 cm\(^2\)
• B. 30.8 cm\(^2\)
• C. 28.8 cm\(^2\)
• D. 57 cm\(^2\)

Hint:

To find the area of a sector, use the formula \(\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2\), where \(\theta\) is the angle and \(r\) is the radius.

Answer 1

The Correct Option is C

The area of a sector of a circle is given by the formula: \[ \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2 \] Here, \(r = 7 \, \text{cm}\) and \(\theta = 72^\circ\). Using \(\pi = \frac{22}{7}\), we substitute the values: \[ \text{Area of sector} = \frac{72}{360} \times \frac{22}{7} \times 7^2 = \frac{1}{5} \times \frac{22}{7} \times 49 = 28.8 \, \text{cm}^2 \] Thus, the correct answer is option (3).