 Let's take a look at another example of a related rate problem. In this one, we are asked how fast is the water level in a cylindrical tank dropping when the radius is 30 centimeters and it is being drained at the rate of 3,000 cubic centimeters per second. Now there's a very important clue in here as to the type of problem it's going to involve. Notice how the rate we are given is in cubic centimeters per second. That cubic centimeters is a volume measurement. So that's really the only clue you're getting that this is going to involve volume of a cylinder. So that's the water and we're told that the water level is dropping and the radius is 30 centimeters. Now remember because it's a cylinder, that radius is never going to change. So that's something we can make use of later because it is going to be constant for this particular scenario. So we can refer to the height perhaps as y. So we'll let y represent however high the water is at any point in time. So now that we've had our picture drawn, let's lay out the rates that were given. So remember that one rate that we're given, the 30,000 cubic centimeters per second, we talked about that being a volume measurement. So let's call that dv dt and because that's the rate at which the water is being drained out, we're going to consider that as a negative quantity. Now what we're trying to find is how fast is the water level dropping. So that would be dy dt at the point in time when r equals 30. Now you might be saying to yourself, well r is always going to be 30. You are correct and so that's something we're going to take into account when we go ahead and set up our equation that we're going to use. Now it would be helpful to remember how to get volume of a cylinder. Remember volume of a cylinder is pi r squared h. But remember you've already noted that the radius is going to be constant here. So we could go ahead and substitute that 30 into your r. So when we do that you have 30 squared, which of course is 900. So the equation we're going to use and remember we refer to the height as y in this particular case. So our equation that we're going to differentiate is simply v equals 900 pi times y. So with our implicit differentiation derivative of v is dv dt. Derivative of 900 pi times y would be 900 pi dy dt. Remember every variable gets differentiated with respect to time. So dv dt remember was that which we were given the negative 3000. So solving for dy dt we have negative 3000 over 900 pi. We can go ahead and simplify that and we'd have negative 10 over 3 pi. You can do that as a decimal if you prefer. It's approximately equal to 1.061. So that rate is of course a negative quantity. So we can conclude that when the radius is 30 centimeters the water level is dropping at a rate of approximately 1.061 centimeters per second. Now take a note about the units of measure on that answer. Remember we were trying to find dy dt and y represents a linear measurement, a height, which is therefore measured in centimeters in this case. That's why it's centimeters per second.