ZOJ 5579 Stean

Stean Time limit: 1 Second Memory Limit: 65536 KB Special Judge

Tom is good at making Stean, he can make Steans of various color and shape. Now he want to know how many water it can contain, and what many material he need to making a stean.

The shape of the Stean follows rules below:

1. The horizontal projection is a circle. The front projection contains and cosine curve. Tom can pour water from the top of Stean.

2.To describe it more clearly, Tom constructs a cylindrical coordinate system. Tom is a strange person, because if there no stean at all when Z1 Z2 are equal to, he still asks. Tom tells you origin of coordinates was on the axis of cylinder, Z -axis is the axis of cylinder. And he measures that the height of undersurface and the height of upsurface of the Z1 Stean Z2 . And he find the formula of cosine curve is R = 2 + cos ( Z ). Here is the R inner circle ' s radius.

Now your need to tell him the capacity and the area of internal surface, which is in direct proportional to water tank cap Acity and material needed. You need to is precise to the digits after the float point.

Input

The first line of the input contains a single integer T (1 <= T <=), which denotes the number of test CA Ses. Then each line contains a case, consisted by a pair of the integer Z1 numbers Z2 and (| | Z1 <= 1000.00, | Z2 | < ; = 1000.00). They is separated by a space.

Output

There T is lines, each line contains a floating point number, the capacity and the area of internal surface. An answer with absolute error less than 10-2 or with relative error less than 10-5 would be accepted.

Sample Input

20 3.14159-0.0001 0.0

Sample Output

44.41 76.280.00 28.27

Author: WANG, Xinglu

Problem solving: Direct integration, pay attention to the size of $z_1 and z_2$, volume can be negative, surface area cannot be negative

1#include <bits/stdc++.h>2 using namespacestd;3 Const DoublePI = ACOs (-1);4 DoubleFuck (Doublez) {5     returnPi* (4*z +4*sin (z) + z/2+ Sin (2*Z)/4);6 }7 DoubleFDoublez) {8     DoubleTMP =2*pi* (2+ cos (z)) *sqrt (1+ sin (z) *sin (z));9     returntmp;Ten } One DoubleSimpsonDoubleADoubleBintn =10000) { A     Const Doubleh = (b-a)/N; -     Doubleans = f (a) +f (b); -      for(inti =1; I < n; i + =2) ans + =4*f (a+i*h); the      for(inti =2; I < n; i + =2) ans + =2*f (a+i*h); -     returnans*h/3; - } - intMain () { +     Doublez1,z2; -     intKase; +scanf"%d",&Kase); A      while(kase--) { atscanf"%LF%LF",&z1,&z2); -         Doublev = Fuck (z2)-fuck (z1); -         DoubleSS = pi* (2+ cos (z1)) * (2+cos (z1)); -         if(Z1 >z2) Swap (Z1,Z2); -         Doubles = Simpson (Z1,Z2) +SS; -printf"%.10f%.10f\n", v,s); in     } -     return 0; to}

View Code

ZOJ 5579 Stean