Awater tank has the shape of an inverted right circular cone with base radius 3 meters and height 6 meters. water is being pumped into the tank at the rate of 12 meters3/sec. find the rate, in meters/sec, at which the water level is rising when the water is 2 meters deep. give 2 decimal places for your answer. type your answer in the space below. if your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).

the rate of change is 3.8m/s

Step-by-step explanation:

The volume of the right circular cone is

The rate of change of volume is

In order to proceed further we have to define r in terms of h so tht we can compute the derivative above.

The ratio between h and r is

Therefore .

We plug that into the derivative above and get:

Thus

Now for the numerical part.

The rate of change of volume is , so when the water is 2 meters deep , therefore:

the answer will be