Math is everywhere around our life. For example, when autumn is coming, the leaves fall from the trees in a beautiful curve.

Today, I am going to talk about an example of a derivative question. Nearby the chemistry building, there is a fountain. Before September, the fountain was empty until one day an operator filled it. This is an interesting mathematical question. We can consider the fountain as a cylinder. We can visually inspect the radius of the fountain is about 5 meters long and the height of it approximately 0.5 meters high. The operator told me that he can fill the fountain about 10 cubic meters per minute. “There is a step in the fountain. I need to fill the water until the water covers the step.” The operator said. This situation makes me interesting. If the step is about 0.3 meters high, how fast is the depth of the water increasing at the moment that the water just covers the step?

First, we have to find the formula of the cylinder volume. Here is the formula, V=(πr^2)h. In this case, we have already known that the radius is constant. Therefore, we just need to substitute r=5 into the equation. Then derivative both sides of the formula, so that we can get dv/dt=(5^2*π)dh/dt. Also, we know that the water would fill around 10 cube meters per minute. So, we can find dh/dt=0.127 m/min.