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`

Answer 1

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