An inverted right circular cone of height 1 meter and base radius of 0.5 meter that is filled with water that is draining out of the bottom out of a hole (circular orifice) of diameter 2cm. What is the level of the water in the tank after two minutes?
I know to use the following formula:
$$\dfrac{dh}{dt}=-\dfrac{A_o}{A_c}\sqrt{2hg}$$
I know now that $A_c=A_c(h)$ now depends on $h$ ($A_c$ is the horizontal cross-section of each slice of the cone). I am also told to ignore the geometrical change that the orifice would make to the cone.
I am teaching myself differential equations but I am having a wicked time with following through on these types of problems. I am pretty good at working with just the formulas of first-order ODEs and using integrating factors but I am lost at this point. Thank you for any input!