CAT 2003 (Retake) QA Question 15 · Geometry - Mensuration

The string tied on the cylinder and the cube is of the same length $\left(n\sqrt{17}\right)$.

Now, we cut the cylinder horizontally such that each turn of the string is now on a separate cylinder. On opening up one of the n cylinders, we get a rectangle whose length is equal to the circumference of the cylinder and whose breadth is equal to h/n. The string will be the diagonal of the rectangle.

Cylinder’s circumference = 2 × π × r = 2 × π × 2/π = 4 units

The string has encircled the cylinder n times, thus the length used in 1 turn

= $\frac{n\sqrt{17}}{n}=\sqrt{17}$

From the above figure,

${\left(\sqrt{17}\right)}^2={\left(\frac{h}{n}\right)}^2+4^2$

∴ h = n

Hence, option (c).