2007/2008 ACM International Collegiate Programming Contest
University of Ulm Local Contest
Problem C: Cylinder
Source file: cylinder.(c|cc|hs|java|pas)
Input file: cylinder.in
Using a sheet of paper and scissors, you can cut out two faces to form a
cylinder in the following way:
- Cut the paper horizontally (parallel to the shorter side) to get two
rectangular parts.
- From the first part, cut out a circle of maximum radius. The circle will
form the bottom of the cylinder.
- Roll the second part up in such a way that it has a perimeter of equal
length with the circle's circumference, and attach one end of the roll to the
circle. Note that the roll may have some overlapping parts in order to get the
required length of the perimeter.
Given the dimensions of the sheet of paper, can you calculate the biggest
possible volume of a cylinder which can be constructed using the procedure
described above?
Input Specification
The input consists of several test cases. Each test case consists of two
numbers w and h (1 ≤ w ≤ h ≤ 100),
which indicate the width and height of the sheet of paper.
The last test case is followed by a line containing two zeros.
Output Specification
For each test case, print one line with the biggest possible volume of the
cylinder. Round this number to 3 places after the decimal point.
Sample Input
10 10
10 50
10 30
0 0
Sample Output
54.247
785.398
412.095
In the first case, the optimal cylinder has a radius of about 1.591549, in
the second case, the optimal cylinder has a radius of 5, and in the third case,
the optimal cylinder has a radius of about 3.621795.