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A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

1. 1/π
2. 2/π
3. 3/π
4. 4/π

Correct answer: 1/π

Solution

The volume of the cylindrical tube is calculated using its height and the radius derived from the circumference formed by the longer edge of the sheet. The cube's volume is derived from its surface area, which equals the area of the sheet. The ratio of these two volumes simplifies to 1/π, making option A the correct choice.

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