A rectangular sheet of paper of size 11 cm × 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:
(a) 1 : 1
(b) 7 : 11
(c) 11 : 7
(d) \frac{11\pi}{7}:\frac{7\pi}{11}
(a) 1 : 1
Explanation:
For the first cylinder:
Height, h = 7 cm
Circumference = 11 cm
⇒ 2πr = 11
⇒ r = \frac{11}{2\pi} cm
For the second cylinder:
Height, H = 11 cm
Circumference = 7 cm
⇒ 2πR = 7
⇒ R = \frac{7}{2\pi} cm
Required ratio = 2πrh : 2πRH
⇒ rh : RH
⇒ \frac{11}{2\pi}\times7:\frac{7}{2\pi}\times11
⇒ 77 : 77
⇒ 1 : 1
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