A Coffee Filter Is in the Shape of a Cone $\sqrt{h}$

Short Answer

A coffee filter is in the shape of a cone, as shown below.Suppose that when it is filled with water to a height h cm, the rate at which coffee flows out the hole at the bottom is given by
Volume of coffee which flows out per second = $\sqrt{h}$ cm³ / sec. Suppose the coffee filter starts full.Write an integral representing the total amount of time it takes for the coffee filter to empty, and then evaluate it to find the time needed for the filter to empty.Give your answer to the nearest second.