calculateVolumeConeInSphere()

Step 1: Understanding the problem

The first step is to understand the problem. We want to calculate the volume of a cone that is inscribed inside a sphere. First, we need to know the formulas for the volume of a sphere and a cone.

The volume of a sphere is calculated using the formula 3/4πr^3, where r is the radius of the sphere.

The volume of a cone is 1/3πr²h, where r is the radius of the base (which is equal to the radius of the sphere) and h is the height of the cone.

 double sphereVolume = 4.0/3.0 * Math.PI * Math.pow(radius,3);
 double coneVolume = Math.PI * radius * radius * height / 3;

Step 2: Sphere and Cone Heights

Since the cone is inside the sphere, the height of the cone is equal to two times the radius of the sphere.

 double coneHeight = 2 * radius;

Step 3: Volume Calculation

Now let's re-calculate the cone volume with the correct height value.

 coneVolume = Math.PI * radius * radius * coneHeight / 3;

Step 4: Calculate Cone Volume

Let's put all this calculation into a function named calculateConeInSphereVolume. This function takes the sphere radius as an argument and returns the cone volume.

 public static double calculateConeInSphereVolume(double radius) {
     double coneHeight = 2 * radius;
     return Math.PI * radius * radius * coneHeight / 3;
 }

Conclusion

In this post, we discussed the steps to calculate the volume of a cone inscribed in a sphere. The steps were explained in details along with the java code snippet at each step for better understanding. Finally, we put together all the code snippets to form a full function to calculate volume. Java Math library was used in this function to calculate powers and pi.