Question

A cylindrical tank with a radius of 4ft is being filled with water at a rate of 2.25f(t³)/(m)in. At what rate is the water level increasing?

Answer 1

The rate at which the water level is increasing in the cylindrical tank is 6.75t²f(t³)/(m)in.

Step-by-step explanation:

To find the rate at which the water level is increasing in the cylindrical tank, we can use the formula:

rate = (change in volume)/(change in time)

Since the radius of the tank is 4ft, the height of the water level is directly proportional to the volume. Therefore, the rate at which the water level is increasing will be the same as the rate at which the volume is increasing.

The rate at which the water is being filled is given as 2.25f(t³)/(m)in. We need to differentiate this function with respect to time to find the rate of change of volume. Differentiating, we get:

rate = 2.25 * (3t²)

So, the rate at which the water level is increasing is 6.75t²f(t³)/(m)in.