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
Options:
(A) 1/π
(B) 2/π
(C) 3/π
(D) 4/π
Official Answer Key:
A
Step-by-Step Solution & Explanation
Step 1 — the cylinder. Joining the two longer edges (each 54 cm) means those edges become the seam running along the tube’s length. Therefore:
Height of cylinder, h = 54 cm
Circumference = the shorter side = 4 cm ⇒ 2πr = 4 ⇒ r = 2/π cm
Volume of cylinder = πr²h = π × (2/π)² × 54 = π × (4/π²) × 54 = 216/π cm³
Step 2 — the cube. Area of the sheet = 54 × 4 = 216 cm²
Surface area of cube = 6a² = 216 ⇒ a² = 36 ⇒ a = 6 cm
Volume of cube = 6³ = 216 cm³
Step 3 — ratio:
(216/π)/216 = 1/π
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