Chapter 11.3, Problem 3QR

To determine

To find: Thearea of a $\frac{\pi }{8}$ radian sector of a circle of radius 8.

Answer to Problem 3QR

The area of the sector is $12.5714\text{sq}\text{.unit}$ .

Explanation of Solution

Given information:

Radius = 8

Sectored angle $=\frac{\pi }{8}$ radian

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 angle of the sector is $\frac{\pi }{8}$ .

Convert into degree

  $\begin{array}{c}\frac{\pi }{8}\text{radian}=\frac{\pi }{8}\times \frac{180°}{\pi }\\ =\frac{45°}{2}\end{array}$

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

  $\begin{array}{c}\text{Area}=\frac{\frac{45°}{2}}{360°}\times \frac{22}{7}\times 8^2\\ =\frac{1}{8}\times \frac{11}{7}\times 64\\ =\frac{88}{7}\\ \approx 12.5714\text{sq}\text{.unit}\end{array}$

Conclusion:

Hence, the required area of the sector is $12.5714\text{sq}\text{.unit}$ .