Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises - Page 610: 7

$$3\pi$$

\begin{align*} s&=\int_{a}^{b} \sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}} d t\\ &=\int_{0}^{\pi} \sqrt{9 \cos ^{2} 3 t+9 \sin ^{2} 3 t} dt \\ &=\int_{0}^{\pi} \sqrt{9\left(\cos ^{2} 3 t+\sin ^{2} 3 t\right)} d t\\ &=\int_{0}^{\pi} 3 \sqrt{\left(\cos ^{2} 3 t+\sin ^{2} 3 t\right)} d t\\ &=3t\bigg|_{0}^{\pi}\\ &=3\pi \end{align*}