Evaporation and Mass#3273
Given a specific vessel, the center is located at the point (0, 0, 0). The vessel extends infinitely upwards, located in the upper half-space relative to the plane. The radius of the vessel's cross-section in the plane is defined by one of the following equations:
The surface of the vessel is formed by rotating the specified curve around the axis.
A liquid with mass is poured into the vessel. It begins to evaporate according to the law v = \alpha S, meaning the evaporation rate is directly proportional to the area of the liquid's open surface (the surface area exposed to air) at any given moment. Determine the time required for the entire liquid to evaporate from the vessel.
The input starts with a single letter "A" or "B", indicating the type of vessel being considered.
For case "A", the following line contains real numbers , , (0 < a, c < 50, 0 \le b \le 50).
For case "B", the next line contains real numbers , (0 < a, b \le 50).
The rd line provides two real numbers (0 < M < 10^4) and (0 < \alpha \le 1).
The liquid's fill height will not exceed 10^{15} units.
Output a single number — the time required for the complete evaporation of the liquid, with an absolute or relative error of 10^{-6}.
Example 1