"**Note**: Click on \"*Kernel*\" > \"*Restart Kernel and Run All*\" in [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) *after* finishing the exercises to ensure that your solution runs top to bottom *without* any errors. If you cannot run this file on your machine, you may want to open it [in the cloud <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_mb.png\">](https://mybinder.org/v2/gh/webartifex/intro-to-data-science/main?urlpath=lab/tree/00_python_in_a_nutshell/06_exercises_volume.ipynb)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 0: Python in a Nutshell (Coding Exercises)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The exercises below assume that you have read the preceeding content sections.\n",
"\n",
"The `...`'s in the code cells indicate where you need to fill in code snippets. The number of `...`'s within a code cell give you a rough idea of how many lines of code are needed to solve the task. You should not need to create any additional code cells for your final solution. However, you may want to use temporary code cells to try out some ideas."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Volume of a Sphere"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The [volume of a sphere <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_wiki.png\">](https://en.wikipedia.org/wiki/Sphere) is defined as $\\frac{4}{3} * \\pi * r^3$.\n",
"\n",
"In **Q2**, you will write a `function` implementing this formula, and in **Q3** and **Q5**, you will execute this `function` with a couple of example inputs.\n",
"\n",
"**Q1**: First, execute the next two code cells that import the `math` module from the [standard library <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/index.html) providing an approximation for $\\pi$!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"import math"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"math.pi"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q2**: Implement the business logic in the `sphere_volume()` function below according to the specifications in the **docstring**!\n",
"\n",
"Hints:\n",
"- `sphere_volume()` takes a mandatory `radius` input and an optional `ndigits` input (defaulting to `5`)\n",
"- Because `math.pi` is constant, it may be used within `sphere_volume()` *without* being an official input\n",
"- The volume is returned as a so-called `float`ing-point number due to the rounding with the built-in [round() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#round) function\n",
"- You may either write your solution as one big expression (where the `...` are) or introduce an intermediate step holding the result before rounding (then, one more line of code is needed above the `return ...` one)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"def sphere_volume(radius, ndigits=5):\n",
" \"\"\"Calculate the volume of a sphere.\n",
"\n",
" Args:\n",
" radius (int or float): radius of the sphere\n",
" ndigits (optional, int): number of digits\n",
" when rounding the resulting volume\n",
"\n",
" Returns:\n",
" volume (float)\n",
" \"\"\"\n",
" return ..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q3**: Execute the function with `radius = 100.0` and 1, 5, 10, 15, and 20 as `ndigits` respectively."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"radius = 100.0"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sphere_volume(...)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sphere_volume(...)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sphere_volume(...)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sphere_volume(...)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"sphere_volume(...)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q4**: What observation do you make?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q4**: Using the [range() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#func-range) built-in, write a `for`-loop and calculate the volume of a sphere with `radius = 42.0` for all `ndigits` from `1` through `20`!\n",
"\n",
"Hint: You need to use the built-in [print() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#print) function to make the return values visible"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"radius = 42.0"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"for ... in ...:\n",
" ..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Q5**: What lesson do you learn about `float`ing-point numbers?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" < your answer >"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the [round() <img height=\"12\" style=\"display: inline-block\" src=\"../static/link/to_py.png\">](https://docs.python.org/3/library/functions.html#round) function, we can see another technicality of the `float`ing-point standard: `float`s are *inherently* imprecise!\n",
"\n",
"**Q6**: Execute the following code cells to see a \"weird\" output! What could be the reasoning behind rounding this way?"
