Chapter 12.4, Problem 1AE

To determine

To find: by what percent the disc method approximates the volume of the sphere.

Answer to Problem 1AE

By $7.25\%$ , the disc method approximates the volume of sphere.

Explanation of Solution

Given information:

Algorithm of the problem to be solved is given:

  

Use $10$ for N and RUN the program.

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 $N=10$ is:

  

From output, the volume calculated by different methods is:

  $\begin{array}{l}\text{Volume of sphere by approximation method}=4492.47\\ \text{Volume of sphere by derived formula}=4188.68\\ \text{Difference in calculation}=\left(4492.47-4188.68\right)\\ =303.79\end{array}$

Calculate difference by percentage:

  $\begin{array}{l}\%\text{Difference}=\frac{303.79}{4188.68}\times 100\\ =0.0725\times 100\\ =7.25\%\end{array}$

Therefore, by $7.25\%$ , the disc method approximates the volume of sphere.