Final answer:
The time required to fill the pond to a level increase of 21 cm is calculated based on the volume of water needed and the current flow rate. To meet the condition of achieving this rise in one hour, the flow rate is recalculated accordingly.
Step-by-step explanation:
To calculate the time required for the level of water in the pond to rise by 21 cm by water flowing through a pipe, we first need to determine the volume of water needed to raise the level. The volume can be calculated using the dimensions of the cuboidal pond, which are 50 m (length) and 44 m (width), with a water level increase of 0.21 m (21 cm). The required volume is thus 50 m × 44 m × 0.21 m.
Next, we convert the flow rate of water from km/hr to m³/s to make the units consistent. A pipe diameter of 4 cm gives an area of π × (0.04 m/2)^2. With the flow at 15 km per hour, we use unit conversion to find the flow in m³/s (by converting km to m and hours to seconds) and then calculate the time by dividing the required volume by the flow rate.
To achieve the rise in water level in exactly one hour, we would adjust the flow rate accordingly. We'd repeat the same volume calculation as above and use the target time of one hour to solve for the new necessary flow rate in m³/s.