A cylindrical tank whose cross-section area is ` 2000 cm^2` has a hole in its bottom ` 1 cm ^2` in area.
(i) If the water is allowed to flow into the tank from a tube above it at the rate of 140 `cm ^3//s`, how high will the water in the tank rise ?
(ii) If the flow of water into the tank is stopped after the above height has been reached, how long will it take for tank to empty itself through the hole?

Explanation

To solve the problem step by step, we will address both parts of the question.

### Part (i): Finding the height of water in the tank

1. **Identify the given values:**
- Cross-sectional area of the tank, \( A = 2000 \, \text{cm}^2 \)
- Area of the hole, \( a = 1 \, \text{cm}^2 \)
- Rate of water inflow, \( Q = 140 \, \text{cm}^3/\text{s} \)
...