calculateVolumeCubeInSphere()

Step 1: Define the Problem

The problem is to find the volume of a cube inscribed in a sphere. To solve this we need first to define the radius of the sphere. The diameter of the sphere is equal to the side length of the cube, and we will use this relationship to find the volume of the cube.

public class Main {
	public static void main(String[] args) {
		double radius = 5;
	}
}

Step 2: Implement the Function for Calculating the Cube Volume

We know that the formula to calculate the volume of a cube is side^3. As the side length of the cube is equal to the diameter of the sphere, this equals 2*radius. Therefore, we could calculate the volume of the cube like this:

public class Main {
	public static void main(String[] args) {
		double radius = 5;
		double volume = Math.pow(2*radius, 3);
	}
}

Step 3: Include a Function to input the Sphere's Radius

We can also create a function to make it more dynamic where we can just input the sphere's radius to get the volume of the cube.

public class Main {
	static double calculateVolume(double radius){
		return Math.pow(2*radius, 3);
	}
	
	public static void main(String[] args) {
		double radius = 5;
		double volume = calculateVolume(radius);
		System.out.println(volume);
	}
}

Step 4: Validation

To make sure our function works correctly, we can validate it using a known example. For a sphere with a radius of 5, the length of the side of the cube is 10, and therefore the volume of the cube is 1000.

public class Main {
	static double calculateVolume(double radius){
		return Math.pow(2*radius, 3);
	}
	
	public static void main(String[] args) {
		double radius = 5;
		double volume = calculateVolume(radius);
		System.out.println(volume);
		assert volume == 1000 : "Test failed!";
	}
}

Conclusion

We have successfully implemented a program to calculate the volume of a cube inscribed in a sphere using Java. This program is flexible and can calculate the volume given any radius of the sphere.

public class Main {
	static double calculateVolume(double radius){
		return Math.pow(2*radius, 3);
	}
	
	public static void main(String[] args) {
		double radius = 5;
		double volume = calculateVolume(radius);
		System.out.println(volume);
		assert volume == 1000 : "Test failed!";
	}
}