Question

Two circular cylinders are formed by rolling two rectangular aluminum sheets each of dimensions 12 m length and 5m breadth, one by Rolling along it's length and the other along it's width. Find the ratio of their Curved Surface Area.

Answer 1

First cylinder: Let first cylinder is obtained by rolling rectangular sheet along it's length.

\(\therefore\) 2πr₁ = 12 m & h₁ = 5 m

⇒ r₁ = \(\frac{12}{2\pi}\) m

∴ Curved surface areas S_F = 2πr₁h₁ = 2π x \(\frac{12}{2\pi}\) x 5 = 60 m²

Second cylinder: let second cylinder is obtained by rolling rectangular sheet along it's width.

∴ 2πr₂ = 5m & h₂ = 12 m

⇒ r₂ = \(\frac5{2\pi}\) m

∴ curved surface area S₂ = 2πr₂h₂ = 2π x \(\frac{5}{2\pi}\) x 12 = 60 m²

required ratio = S

Alternative :

curved surface area of both cylinder is equal to the area of rectangular sheet. because both cylinders are obtained by rolling it. Hence, carved surface area of both cylinder are equal. of carved surface area of both cylinder is 1 :1