Question

Water is flowing at the rate of 4 km/h through a pipe of radius 7 cm into a rectangular tank with length and breadth as 25 m and 22 m, respectively. The time (in hours) in which the level of water in the tank will rise by 28 cm is (take \( \pi = \frac{22}{7} \)):

• A. \( \frac{2}{3} \)
• B. \( \frac{2}{2} \)
• C. \( \frac{3}{2} \)
• D. \( \frac{3}{3} \)

Hint:

Always make sure to convert all units properly before solving for time or other quantities. In this case, converting km/h to cm/h was important to keep the units consistent.

Answer 1

The Correct Option is B

The volume of water flowing per hour through the pipe is given by: \[ V = \pi r^2 v \] where: - \( r = 7 \) cm is the radius of the pipe, - \( v = 4 \) km/h is the velocity of water (convert to cm/h: \( 4 \times 10^5 \) cm/h). The volume of water that raises the level in the tank by 28 cm is given by: \[ V_{\text{tank}} = \text{Length} \times \text{Breadth} \times \text{Height increase} = 25 \times 22 \times 28 \, \text{cm}^3 \] Equating the two volumes and solving for the time gives the correct answer. Thus, the time in hours is \( \frac{2}{2} \).