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…

In first case :

Height of cylinder (h) = 7 cm

Let radius be r cm

⇒ 2πr = 11

⇒ r = $\frac{11}{2π}$

In second case :

Height of cylinder (H) = 11 cm

Let radius be R cm

⇒ 2πR = 7

⇒ R = $\frac{7}{2π}$

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

Hence, Option 1 is the correct option.