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CAT-2003-Previous Years Paper
Consider a cylinder of height h cm and radius r = 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).
The same string, when wound on the exterior four walls of a cube of side n cm, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale). The length of the string is
A B C n cm D
The four faces through which a string is passing can be shown as
Therefore, the length of the string in each face
Therefore, the length of the string through four faces =