A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly six complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder).
How long is the string in cm?

Correct answer:

x =  180 cm

Step-by-step explanation:

$$\begin{gathered} h=108\text{cm} \\ c=24\text{cm} \\ c=2\pi \cdot r \\ r=c/(2\pi )=24/(2\cdot 3.1416)\doteq 3.8197\text{cm} \\ x=\sqrt{h^2+(6\cdot c{)}^2}=\sqrt{108^2+(6\cdot 24{)}^2}=180\text{cm} \end{gathered}$$

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