A rectangular sheet of paper of size 11 cm x 7 cm is first rotated about the side 11 cm and then about the side 7 cm to form a cylinder, as shown in the diagram. The ratio of their curved surface areas is:

1. 1 : 1

2. 7 : 11

3. 11 : 7

4. $\dfrac{11π}{7} : \dfrac{7π}{11}$

In first case :

Height of cylinder (h) = 7 cm

Let radius be r cm

⇒ 2πr = 11

⇒ r = $\dfrac{11}{2π}$

In second case :

Height of cylinder (H) = 11 cm

Let radius be R cm

⇒ 2πR = 7

⇒ R = $\dfrac{7}{2π}$

$\therefore \dfrac{\text{CSA of 1st cylinder}}{\text{CSA of 2nd cylinder}} = \dfrac{2πrh}{2πRH} \\[1em] = \dfrac{rh}{RH} \\[1em] = \dfrac{\dfrac{11}{2π} \times 7}{\dfrac{7}{2π} \times 11} \\[1em] = \dfrac{\dfrac{77}{2π}}{\dfrac{77}{2π}} \\[1em] = \dfrac{1}{1} \\[1em] = 1 : 1.$

Hence, Option 1 is the correct option.