#### Answer

$$3\pi$$

#### Work Step by Step

\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*}