Consider a cylinder of height $h$ cm and radius $r = \dfrac2π$ cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of $n$ turns (in other words, the string's length is the minimum length required to wind $n$ turns)
In light of my previous question it has a second part.
$2.)$The same string, when wound on the four exterior four walls of a cube of side $n$ cm, starting at point C and ending at point D, can give exactly one turn (as shown in the below figure).The length of the string in cm is ?
By opening the cube the skeleton will look like the above with string in red color.
Options
$a.)\quad \sqrt2\cdot n\\ \color{green}{b.)\quad\sqrt{17}n}\\ c.)\quad n\\ d.)\quad\sqrt{13}n$
$3.)$ And hence now conclude the from problem $1.)$ and $2.)$ relation between $h$ and $n$.?
Options
$a.)\quad h=\sqrt2\cdot n\\ b.)\quad h=\sqrt{17}\\ \color{green}{c.)\quad h=n}\\ d.)\quad h=\sqrt{13}n$
from the previous question length $=\sqrt{h^2 + 16 n^2}$. Now how do i use the data with the occurence of cube of side $n$ cm