Question

The dimension of a rectangular tank filled with water is 50m × 16m × 60m. At a certain instant, the tank begins to drain. Find the rate at which the volume of water is drained if the depth of water is changing at a rate of 12 m/min.

Answer 1

To calculate the rate at which water is drained from the tank, multiply the surface area of the tank (length x width) by the rate at which the depth of water is decreasing. The flow rate is 9600 m³/min.

Step-by-step explanation:

The question concerns the rate at which water is being drained from a rectangular tank. We know the tank measures 50m x 16m x 60m and that the depth of water decreases at a rate of 12 m/min. To find the rate at which the volume of water is decreasing, we must calculate the volume change per minute.

Since the surface area (length x width) of the tank remains constant, and only the depth is changing, we can use the formula for the rate of change of volume (dV/dt) as follows:

dV/dt = area × rate of change of depth

dV/dt = 50m × 16m × 12 m/min

Therefore, the rate at which the volume of water is drained (also known as the flow rate) is 9600 m³/min.