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Question
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 ______.
Options
1 : 1
7 : 11
11 : 7
`(11π)/7 : (7π)/11`
Solution
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 1 : 1.
Explanation:
In first case, height of cylinder (h) = 7 cm
Circumference of cylinder (2πr) = 11
Then, curved surface area
C1 = 2πrh
= 11 × 7
= 77 cm
In second case, height of cylinder (H) = 11 cm
Circumference of cylinder (2πR) = 7
Then, curved surface area,
C2 = 2πRH
= 7 × 11
= 77 cm
Then, C1 : C2
= 77 : 77
= 1 : 1
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