Two rectangular sheets of paper, each 60 cm × 36 cm, are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5 : 3.
Let's analyze the two scenarios:
Scenario 1: Rolling along the length
The circumference of the base of the cylinder becomes 60 cm.
The height of the cylinder becomes 36 cm.
Let the radius of the base = R
Then, 2πR = 60
⇒ R = 30/π
Scenario 2: Rolling along the breadth
The circumference of the base of the cylinder becomes 36 cm
The height of the cylinder becomes 60 cm.
Let the radius of the base be r.
Then, 2πr = 36
⇒ r = 18/π
Calculating the volumes:
Volume of cylinder 1 = πR2h1 = π(30/π)2 × 36 = 32400/π
Volume of cylinder 2 = πr2h2 = π(18/π)2 × 60 = 19440/π
Ratio of volumes:
Volume of cylinder 1 / Volume of cylinder 2 = (32400/π) / (19440/π) = 5/3
Therefore, the ratio of the volumes of the two cylinders is 5 : 3.