CAT 2003 Slot 2 — QA Question 14
Answer the following question based on the information given below.
Consider a cylinder of height h cms and radius r = 2/π cms 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 cms, 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, in cms, is
Answer & solution
- A
- C
n
- D
If the cube is cut open as shown in the figure below, a rectangle with sides 4n and n is obtained.
The string is the diagonal along this rectangle, with length,
∴ The length of the string is
Hence, option (b).