The area of the sector of a circle with radius 7 cm and of angle 60° is

Correct option is B

Given:

1. Radius of the circle: r = 7 cm

2. Central angle: $$\theta$$​ = $$60^\circ$$​​

Formula Used:

The area of a sector is calculated as:

​$$\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2$$​​

Solution:

1. Substitute values into the formula:

​$$\text{Area of Sector} = \frac{60}{360} \times \pi \times 7^2$$​​

2. Simplify the fraction:

​$$\frac{60}{360} = \frac{1}{6}$$​​

3. Calculate $$r^2$$​:

​$$7^2$$​ = 49

4. Substitute the values:

​$$\text{Area of Sector} = \frac{1}{6} \times \pi \times 49$$​​

​$$\text{Area of Sector} = \frac{49\pi}{6}$$​​

5. Substitute $$\pi = \frac{22}{7}$$​:

​$$\text{Area of Sector} = \frac{49 \times \frac{22}{7}}{6}$$​​

​$$\text{Area of Sector} = \frac{49 \times 22}{7 \times 6}$$​​

​$$\text{Area of Sector} = \frac{1078}{42}$$​​

​$$\text{Area of Sector} = \frac{77}{3} \text{cm}^2$$​​

Final Answer:

The correct option is:

​$$B: \frac{77}{3} \text{cm}^2$$​​