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?
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
- 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.