In this problem, you are required to use the Monte Carlo Method to estimate the volume of the following object

Please write pyspark codes to compute the volume using the approaches:

1. In the first approach, you should use the DataFrame API of pyspark. For help, a good reference is the pyspark example in /spark/examples/src/main/python/pi.py (in your folder of spark) to estimate the value of using the Monte Carlo method.

2. In the second approach, you should use Spark Streaming API or Structured Streaming API. The idea is that you need to create an input stream of random points in a fixed region while counting the cumulative number of points inside each of the objects. The requirement is that you should only use one input stream to compute the volumes of the objects all together instead of using one input stream for each object. On the other hand, the way to create such an input stream is up to you. For example, you may use stream sockets or RDD queues. Moreover, you may consider to use the methods flatMap() and updateStateByKey().

Please provide both your codes and your demonstration of the results. Take screenshots whenever necessary.

The first object, denoted by Ox, is a sphere centered at (0, 1, -2) of radius 4. As a set of points, we write 0 A = {(1,y,z) x2 + (y - 1)2 + (x + 2)2