Computer Sciences > Gate 2024 Set-1 > Fill in the Blanks
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
Correct : a
Given: Rectangle dimensions = 54 cm × 4 cm
Area of rectangular sheet = 54 × 4 = 216 cm²
Form the cylinder
When the two longer edges (54 cm) are joined:
• The 4 cm side wraps around to form the circumference
• Height of cylinder = 54 cm
• Circumference = 4 cm
Radius of cylinder
2πr = 4
r = 2/π cm
Volume of cylinder
Volume = πr²h
Volume = π × (2/π)² × 54
Volume = π × (4/π²) × 54
Volume = 216/π cm³
Side of cube
Surface area of cube = 6a² = 216
a² = 36
a = 6 cm
Volume of cube = a³ = 6³ = 216 cm³
Ratio = (216/π) ÷ 216
Ratio = 216/(216π)
Ratio = 1/π
Answer: A) 1/π
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