Answer
The length of the slide is $~~4.1~m$
Work Step by Step
We can find the angle $\theta$ that is subtended by the slide:
$sin~\theta = \frac{4.0~m}{12~m}$
$\theta = sin^{-1}~\frac{4.0~m}{12~m}$
$\theta = 19.47^{\circ}$
We can find the length of the slide:
$L = \frac{19.47^{\circ}}{360^{\circ}}~(2\pi)(12~m)$
$L = 4.1~m$
The length of the slide is $~~4.1~m$
