Water is following at the rate of 5 km/hr. through a cylindrical pipe of diameter 14 cm. into a rectangular tank which is 50 m. long and 44 m wide. Find the time in which the level of water in the tank will rise by 7 cm.
B
Correct answer
Explanation
Water flows through cylindrical pipe at 5 km/hr. Pipe diameter = 14 cm, so radius = 7 cm = 0.07 m. Volume of water flowing per hour = π × r² × length = π × (0.07)² × 5000 m³ (converting 5 km to 5000 m). This is π × 0.0049 × 5000 = 24.5π m³/hr. Tank dimensions: 50 m × 44 m, rise needed = 7 cm = 0.07 m. Volume needed = 50 × 44 × 0.07 = 154 m³. Time = Volume needed / Flow rate = 154 / (24.5π) hours. Using π ≈ 22/7: 24.5π = 24.5 × 22/7 = 77. So Time = 154 / 77 = 2 hours. The answer is 2 hours.