Water is dripping out from a conical funnel of semi-vertical angle `pi/4` at the uniform rate of `2c m^2//s e c` in its surface area through a tiny hole at the vertex in the bottom. When the height of the water is 4cm, find the rate of decrease of the height of the water.

Explanation

To solve the problem step by step, we need to find the rate of decrease of the height of the water in a conical funnel when the height of the water is 4 cm. We are given that the water is dripping out at a rate of 2 cm³/s.

### Step 1: Understand the Geometry of the Cone
The cone has a semi-vertical angle of \(\frac{\pi}{4}\). This means that the radius \(R\) and height \(H\) of the cone are equal when the cone is filled to a certain height \(h\).

### Step 2: Relate the Volume of the Cone to Height
The volume \(V\) of a cone is given by the formula:
\[
...