Chapter 11.3, Problem 2QR

To determine

To find: Thearea of a $30°$ sector of a circle of radius 6.

Answer to Problem 2QR

The area of the sector is $\frac{66}{7}sq\text{.unit}$ .

Explanation of Solution

Given information:

Radius = 6

Sectored angle $=30°$

Formula used:

Area of a sector with angle $\theta$ and the radius $r$ :

  $\text{Area}=\frac{\theta }{360°}\times \pi r^2$

Calculation:

Given that the radius is 6 and the angle is $30°$ .

Now, calculate the area. Use the formula $\text{Area}=\frac{\theta }{360°}\times \pi r^2$ .

  $\begin{array}{c}\text{Area}=\frac{30°}{360°}\times \frac{22}{7}\times 6^2\\ =\frac{1}{12}\times \frac{22}{7}\times 36\\ =\frac{66}{7}\end{array}$

Conclusion:

Hence, the required area of the sector is $\frac{66}{7}sq\text{.unit}$ .