Answer
$$\frac{5 \pi}{2}$$
Work Step by Step
Since
$$\mathbf{r}=(4 \cos t) \mathbf{i}+(4 \sin t) \mathbf{j}+3 t \mathbf{k} $$
Then \begin{align*}
\mathbf{v}&=(-4 \sin t) \mathbf{i}+(4 \cos t) \mathbf{j}+3 \mathbf{k} \\ |\mathbf{v}|&=\sqrt{(-4 \sin t)^{2}+(4 \cos t)^{2}+3^{2}}\\
&=\sqrt{25}=5 \end{align*}
Hence
\begin{align*}
s(t)&=\int_{0}^{t} 5 d \tau\\
&=5 t \\
\text{ Length }&=s\left(\frac{\pi}{2}\right)\\
&=\frac{5 \pi}{2}\end{align*}
