# If a cylindrical tank with radius 5 meters is being filled with water at a rate of 3 cubic meters per minute, how fast is the height of the water increasing?

##### 1 Answer

The answer is

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

In the problem, we are given

In general

- find a formula to relate the 2 variables

- substitute values to remove the constant variables

- implicitly differentiate wrt time (most often the case)

- substitute the given rate

- and solve for the desired rate.