Chapter 15, Problem 33CR

To determine

To Find: Theratio of the length of arc and the diameter.

Answer to Problem 33CR

  $\frac{AC}{ARC}=\frac{2}{\pi }$

Explanation of Solution

Given:

  

Formula Used:

  $\begin{array}{l}\text{Semi-Perimeter}=\frac{2\pi r}{2}\\ \text{Length of diameter }=2\times Radius\\ \text{Length of an arc}=angle\times radius\end{array}$

Calculation:

  $\begin{array}{l}let\\ \text{Length of }AOber\\ \text{Length of }AC=2r\\ \text{Length of Arc}=\frac{2\pi r}{2}\\ AC=2r\\ ARC=\frac{2\pi r}{2}=\pi r\\ \frac{AC}{ARC}=\frac{2r}{\pi r}\\ \text{⇒}\frac{AC}{ARC}=\frac{2}{\pi }\end{array}$

Conclusion:

Thus, the ratio of arc and diameter is $\frac{AC}{ARC}=\frac{2}{\pi }$ .