Cylinder helix length

A regular helix is drawn on the shell of the cylinder such that it wraps around the cylinder precisely three times (that is, the point where it touches the upper base is exactly above the point where it touches the lower base). If the diameter of the cylinder is equal to 2 and its height is 3, then the length of the helix is:

Final Answer:

d =  19.0868

Step-by-step explanation:

$$\begin{gathered} D=2 \\ h=3 \\ r=D/2=2/2=1 \\ n=3 \\ o=\pi \cdot D=3.1416\cdot 2\doteq 6.2832 \\ a=n\cdot o=3\cdot 6.2832\doteq 18.8496 \\ {a}^2+h^2=d^2 \\ d=\sqrt{a^2+h^2}=\sqrt{18.8496^2+3^2}=19.0868 \end{gathered}$$

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