Question

If the angle of sector is 30°, then the area of a sector of the circle with radius 7 cm is___(use \(\pi = \frac{22}{7}\))

• A. \(\frac{77}{6} \text{ cm}^2\)
• B. \(\frac{77}{8} \text{ cm}^2\)
• C. \(\frac{132}{7} \text{ cm}^2\)
• D. \(\frac{154}{6} \text{ cm}^2\)

Answer 1

The Correct Option is A

To solve the problem, we need to find the area of a sector of a circle with radius 7 cm and a central angle of \(30^\circ\), using \( \pi = \frac{22}{7} \).

1. Understanding the Sector Area Formula:
The area \(A\) of a sector of a circle is given by:

\[ A = \frac{\theta}{360} \times \pi r^2 \]
where:
\(\theta = 30^\circ\), \(r = 7 \, \text{cm}\), \(\pi = \frac{22}{7}\)

2. Substituting the Values:
\[ A = \frac{30}{360} \times \frac{22}{7} \times 7^2 \]

3. Simplifying the Expression:
\[ A = \frac{1}{12} \times \frac{22}{7} \times 49 \]

4. Canceling and Multiplying:
\[ A = \frac{1}{12} \times \frac{1078}{7} = \frac{22 \times 7}{12} = \frac{154}{12} \]

5. Reducing the Fraction:
\[ A = \frac{77}{6} \, \text{cm}^2 \]

Final Answer:
The area of the sector is \({\frac{77}{6} \, \text{cm}^2} \).