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If two rectangular sheets each of dimensions 2x and 2y form the curved surfaces of two different cylinders, then the ratio of the quotient of the volumes \(\big(\frac{V_1}{V_2}\big)\) to that of the areas of the curved surfaces \(\big(\frac{S_1}{S_2}\big)\) of the two cylinders is 

(a) \(\frac{x^2}{y}:1 \) or \(\frac{y^2}{x}:1 \)

(b)  \(\frac{2x}{y}:1 \) or \(\frac{2y}{x}:1 \)

(c) \(\frac{3x}{y}:1 \) or \(\frac{3y}{x}:1 \)

(d) \(\frac{x}{y}:1 \) or \(\frac{y}{x}:1 \)

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(d)  \(\frac{x}{y}:1 \) or \(\frac{y}{x}:1 \)

Let the radii of the two cylinders be r1 and r2 respectively. 

Then, 2πr1 = 2x and 2πr2 = 2y 

⇒ r1 = \(\frac{x}{π}\)   and r2 = \(\frac{y}{π}\) 

Also, the height h1 = 2y and h2 = 2x

∴ If V1, V2 and S1, S2 be the respective volumes and curved surface areas of these cylinders, then,

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