A rectangular sheet of length 28 cm and breadth 16 cm is folded to meet the edges so that it is made into a cylindrical pipe in two possible ways – one along the length and the other along the breadth. The larger volume is how much percentage of smaller volume?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 175%.
Circumference = 28 ⇒ 2πr = 28 ⇒ r = 28 ÷ (2π) = 14/π
Height = breadth = 16
Volume = πr²h = π × (14/π)² × 16 = (196/π) × 16 = 3136/π
Circumference = 16 ⇒ 2πr = 16 ⇒ r = 8/π
Height = length = 28
Volume = πr²h = π × (8/π)² × 28 = (64/π) × 28 = 1792/π
Larger volume = 3136/π
Smaller volume = 1792/π
Ratio = 3136 : 1792 = 49 : 28 = 7 : 4
Percentage = [(7 − 4)/4] × 100 = (3/4) × 100 = 75% more = 175%