/*
    CalculateSphereVolume.java
    CIS 160
    David Klick
    2004-11-21

    This program uses a calculus-style technique to determine the
    volume of a sphere. The sphere is sliced into disks which we
    can use to roughly approximate the volume. Each successive
    volume calculation slices the sphere into twice as many pieces,
    which makes the volume calculation increasingly accurate. When
    two successive volume calculations fall within the acceptable
    tolerance level, then the program is done.

    The program then displays how the volume is related to Pi * r^3.
    We know that the area of a circle is Pi * r^2, so the volume
    must be related to Pi * r^3 by some factor. The answer should,
    of course, be a number close to 4/3 (1.33333...).

    It should be noted that we get our initial upper bound for the
    volume of the sphere by calculating the volume of its bounding
    cylinder (Pi * r^2 * 2r). Every successive calculation produces
    a smaller and smaller number for the volume. If you want a more
    precise answer, just change the value of the variable "tolerance",
    recompile, and rerun the program.
*/

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.IOException;

public class CalculateSphereVolume {
    public static void main(String[] args) throws IOException {
        BufferedReader kbd = new BufferedReader(
            new InputStreamReader(System.in));
            
        double oldVolume = 0.0;
        double newVolume = 0.0;
        double radius = 0.0;
        int steps = 1;
        double change = 0.0;
        double tolerance = 0.0000001;

        while (true) {
            try {
                System.out.print("Enter radius of sphere: ");
                radius = Double.parseDouble(kbd.readLine());
                break;
            } catch (NumberFormatException e) {
                System.out.println("Error: Invalid number!");
            }
        }

        // only allow positive radius
        radius = Math.abs(radius);
        
        // start with volume of the bounding cylinder
        newVolume = 2.0 * Math.PI * radius * radius * radius;
        
        do {
            oldVolume = newVolume;
            steps *= 2;
            double width = radius / steps;
            double x = width / 2.0;

            newVolume = 0.0;
            for (int i=1; i<=steps; x+=width, i++)
                newVolume -= x * x;
            newVolume = (newVolume + radius * radius * steps)
                * 2 * Math.PI * width;
            System.out.println("Volume = " + newVolume
                + " (steps: " + steps + ")");
            change = Math.abs(newVolume - oldVolume);
        } while (change > tolerance);

        double factor = newVolume / (Math.PI * radius * radius * radius);
        System.out.println("\n\n" + factor + " times PI * r^3"); 
    }
}