A rectangular sheet is of length x and breadth y. If p is the volume of the cylinder formed by rolling the sheet along its breadth and q is the volume of the cylinder formed by rolling the sheet along its length, and q=2p, then which one of the following is correct?

Explanation

Rolling along breadth makes the height x and circumference y, so volume p = \frac{y^2 x}{4\pi}. Rolling along length makes height y and circumference x, so volume q = \frac{x^2 y}{4\pi}. Given q = 2p \implies \frac{x^2 y}{4\pi} = 2 \left(\frac{y^2 x}{4\pi}\right). Simplifying yields x = 2y.

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