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#### Overview of this book

Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you’ll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges.
Table of Contents (14 chapters)
Preface
1. Fundamentals of Python
Free Chapter
2. Python's Main Tools for Statistics
3. Python's Statistical Toolbox
4. Functions and Algebra with Python
5. More Mathematics with Python
6. Matrices and Markov Chains with Python
7. Doing Basic Statistics with Python
8. Foundational Probability Concepts and Their Applications
9. Intermediate Statistics with Python
10. Foundational Calculus with Python
11. More Calculus with Python
12. Intermediate Calculus with Python

# 10. Foundational Calculus with Python

## Activity 10.01: Maximum Circle-to-Cone Volume

Solution:

1. To find the volume of the resulting cone, you need the height of the cone and the radius of the base, as in the figure on the right of Figure 10.33. First, we find the circumference of the base, which is equal to the arc length AB in the cut circle on the left. You can set R to `1` since all we're interested in is the angle.

Radian measurements make finding arc lengths easy. It's just the angle left over from the cut, which is 2π - θ times the radius R, which we're setting to `1`. So θ is also the circumference of the base of the cone. We can set up an equation and solve r:

Figure 10.34: Formula to calculate the radius

2. We'll code that into our program. We'll need to import a few things from Python's `math` module and define the `r` variable:
```from math import pi,sqrt,degrees
def v(theta):
r = (2*pi - theta)/(2*pi) ```
3. ...