Candy floss

The volume of a cylinder is given by cross-sectional area $\times$ length, so $\pi r^2\times \text{length}$. 

Working in mm, the original cylinder of sugar has volume $\pi \left(\dfrac{30}{2}\right)^2\times 40mm^3$

Finding the volume of sugar as a number

$\pi \left(\dfrac{30}{2}\right)^2\times 40=\pi\dfrac{30^2}{4}\times40=\pi\times900\times10=9000\pi$.

The cylinder of candy floss has volume $\pi \left(\dfrac{1}{2}\right)^2 x$, so $$\begin{align}\pi \left(\frac{1}{2}\right)^2 x=&9000\pi\\

\Rightarrow\pi\times\frac{1}{4}x=&9000\pi\\

\Rightarrow x=&9000\times4\\

\Rightarrow x=&36000\end{align}$$So $x=36000$mm, or $36$m.

Using algebra to find the length directly

The cylinder of candy floss has volume $\pi \left(\dfrac{1}{2}\right)^2 x$, so $$\begin{align}\pi \left(\frac{1}{2}\right)^2 x&=\pi \left(\frac{30}{2}\right)^2\times 40\\

\Rightarrow 1^2x&=30^2\times40\\

\Rightarrow x&=36000\end{align}$$

So $x=36000$mm, or $36$m.

Using scale factors of enlargement

The ratio of the diameters of the cylinders is 1:30,

so the ratio of the cross-sectional areas is 1:900,

so the height of the thin cylinder will need to 900 times longer than the height of the fat cylinder.

Therefore the height of the thin cylinder is 36m long.