Evaporation and Height#3271
A vessel is described with its center at the point (0, 0, 0). This vessel extends infinitely in height and is situated above the half-space of the plane. The radius of the vessel's cross-section on the plane is defined by one of the following equations:
The vessel's surface is formed by rotating the specified curve around the axis.
Liquid is poured into the vessel up to a height . It then begins to evaporate according to the law v = \alpha S, where the evaporation rate is directly proportional to the area of the liquid's exposed surface (the surface area in contact with air) at any given time. Determine the time required for all the liquid to evaporate from the vessel.
The input starts with a single letter ", , or ", indicating the type of vessel being considered.
For case "", the next line provides real numbers a, b, c (0 < a, c \leq 10^2, 0 \leq b \leq 10^2).
For case "", the next line also provides real numbers a, b, c (0 < a, c \leq 10^2, 0 \leq b \leq 10^2).
For case "", the next line contains real numbers (0 < a, b \leq 10^2).
The rd line provides two real numbers: (0 < H < 10^4) and (0 < \alpha \leq 1).
Output a single number — the time required for all the liquid to evaporate, with an absolute or relative error of 10^{-6}.
Example 1