Final answer:
The rate at which water is drained from a rectangular tank measuring 50m × 16m × 60m, with a depth changing at a rate of 12 m/min, is -9,600 m³/min.
Step-by-step explanation:
The rate at which the volume of water is drained from a rectangular tank can be found by using the formula for the volume of a rectangular prism, which is Volume = length × width × height. However, since only the depth of the water is changing, we only need to consider the rate at which the height is decreasing. The dimensions of the tank are given as 50m × 16m × 60m, but since height is the only dimension changing, the rate of change of the volume is equal to the area of the base times the rate of change of the height.
The base area is 50m × 16m = 800m². With a rate of change of the depth of 12 m/min, the rate at which the volume of water is drained is Volume rate = base area × rate of change of height = 800m² × 12 m/min = 9,600 m³/min. Therefore, the correct answer is D) -9,600 m³/min. We use a negative sign to indicate that the volume of water is decreasing.