Question

If the diameter of a circle is 6 inches, how long is the arc subtended by an angle measuring 70°?

Answer 1

Since the diameter of the circle is 6 inches, then the radius will be half that, or 3 inches,

$\bf \textit{arc's length}\\\\ s=\cfrac{r\pi \theta }{180} \quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta =70 \end{cases}\implies s=\cfrac{3\cdot \pi \cdot 70}{180}\implies s=\cfrac{7\pi }{6}$