Chapter 11, Problem 13MCQ

To determine

To calculate: A expression for the perimeter of the sector in terms of $r$.

Answer to Problem 13MCQ

The perimeter of the sector of the cicle is $P=\frac{\pi r}{6}$

Explanation of Solution

Given information: A sector of a circle has a central angle measure of ${30}^0$ and radius $r$.

Concept Used:

The ratio of the perimeter $P$ of a sector to the perimeter of the whole circle ( $2\pi r$ ), is equal to the ratio of the degree measure of the sector to $360$ .

  $\frac{P}{2\pi r}=\frac{x}{360}$

  $P=\frac{x}{360}\times 2\pi r$ , where $x$ is the central angle of sector in degree.

Calculation:

A circle of radius $r$ and sector has central angle ${30}^0$

The perimeter of sector of cicle is:

  $P=\frac{x}{360}\times 2\pi r$

Here in this question the $x$ is equal to ${30}^0$

  $P=\frac{30}{360}\times 2\pi r$

  $P=\frac{2\pi r}{12}$

  $P=\frac{\pi r}{6}$

The perimeter of the given sector of circle is $P=\frac{\pi r}{6}$

Conclusion:

The perimeter of the sector of the cicle is $P=\frac{\pi r}{6}$