A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer…
2024
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
- A.
1/π
- B.
2/π
- C.
3/π
- D.
4/π
Attempted by 38 students.
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Correct answer: A
Key steps: identify cylinder dimensions from the sheet and compute both volumes.
Cylinder dimensions: When the two longer edges (54 cm) are joined, the height of the cylinder is 54 cm and the circumference is 4 cm. Thus radius r = 4/(2π) = 2/π cm.
Cylinder volume: V_cyl = πr²h = π*(2/π)²*54 = π*(4/π²)*54 = 216/π cm³.
Cube volume: Sheet area = 54×4 = 216 cm². For a cube, surface area = 6a² = 216 ⇒ a² = 36 ⇒ a = 6 cm. So V_cube = a³ = 216 cm³.
Ratio: V_cyl / V_cube = (216/π) / 216 = 1/π.
Answer: 1/π
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