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CAT 2003 Slot 2 — QA Question 14

Basics of Mensuration/PrismEasy
Passage / Data

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

Correct answer: 17 n

  • A

    2n

  • 17n

  • C

    n

  • D

    13n

Solution

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,

n2+(4n)2=n17

∴ The length of the string is n17.

Hence, option (b).

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CAT 2003 Slot 2 QA Q14: The same string, when wound on the exterior four walls of a cube of side n cms, starting at point C and ending — Solution | TheCATExam