Question

A string with endpoints E and R is to wrapped around the circumference of circle D, as indicated by the dashed arcs. What must be the length of the string on segment ER so that E’ is wrapped onto point Q?

Answer 1

Let's begin by identifying key information given to us:

$\begin{gathered} Radius=5units \\ m\angle RDQ=\frac{5}{4}\pi rad \\ \frac{5}{4}rad\times\frac{180}{\pi}=71.61972\approx72^{\circ} \\ ER=xunits \\ \\ \text{The length of the arc is given by:} \\ s=r\theta\Rightarrow5\cdot\frac{5}{4}\pi=\frac{25}{4} \\ s=\frac{25}{4}\pi units \\ s=E^{\prime}Q=\frac{25}{4} \\ \\ \therefore E^{\prime}Q=\frac{25}{4}\pi units \end{gathered}$

Hence, the correct answer is 25/4 pi units