Chapter 12.4, Problem 2AE

To determine

To find: the total volume of $n$ discs for each value of $n$ by running the given program.

Answer to Problem 2AE

The volume of sphere calculated by approximation method of $20,50,100\text{ and }1000$ discs are $4343.25,4251.2,4220.1\text{ and }\mathrm{4191.92.}$

Explanation of Solution

Given information:

Algorithm of the problem to be solved is given:

  

Calculation:

Write the program in any programming language (here, C++ language is used) using algorithm and RUN it.

The program looks like:

  

The output of the program when $N=20$ is:

  

The output of the program when $N=50$ is:

  

The output of the program when $N=100$ is:

  

The output of the program when $N=1000$ is:

  

Therefore, from output, the volume of sphere calculated by approximation method of $20,50,100\text{ and }1000$ discs are $4343.25,4251.2,4220.1\text{ and }\mathrm{4191.92.}$

As the number of discs’ increases, the approximate volume approaches the actual volume.