Worked Examples: Using Python as a Calculator#
These worked solutions correspond to the exercises on the Using Python as a Calculator page.
How to use this notebook:
Try each exercise yourself first before looking at the solution
The code cells show both the code and its output
Download this notebook if you want to run and experiment with the code yourself
Your solution might look different - that’s fine as long as it gives the correct answer!
Setup#
We’ll import the math
module once here at the beginning. In a Jupyter notebook, once you import a module in a cell and run that cell, the module remains available for all subsequent cells in the same session.
import math
Exercise 1: Volume of a Sphere#
Problem: Calculate the volume of a sphere with a radius of 5 units. Use math.pi
and the formula
Solution:
import math
(4 / 3) * math.pi * 5**3
523.5987755982989
Explanation:
We use
math.pi
to get the value of \(\pi\)The radius is 5, so we calculate \(r^3\) using
5**3
We calculate \(\frac{4}{3}\) using
4 / 3
(which gives a float: 1.333…)Following the order of operations (BODMAS), this evaluates to approximately 523.60 cubic units
Key concept: Python’s **
operator is used for exponentiation (raising to a power).
Exercise 2: Degrees to Radians#
Problem: Convert 45 degrees to radians using math.radians()
.
Solution:
import math
math.radians(45)
0.7853981633974483
Explanation:
The
math.radians()
function converts degrees to radiansWe pass 45 as the argument to convert 45°
The result is approximately 0.7854 radians, which equals \(\frac{\pi}{4}\)
Why radians matter: Python’s trigonometric functions expect angles in radians, not degrees.
Verification: We can check that this equals π/4:
import math
math.pi / 4
0.7853981633974483
They match!
Exercise 3: Logarithm Base 2#
Problem: Calculate log base 2 of 32 using math.log(x, base)
.
Solution:
import math
math.log(32, 2)
5.0
Explanation:
math.log(x, base)
calculates the logarithm of the first argument with the specified baseWe’re finding \(\log_2(32)\), which asks: “2 to what power equals 32?”
The answer is 5.0 because \(2^5 = 32\)
Verification: Let’s confirm that \(2^5 = 32\):
2**5
32
Note: If you don’t specify a base, math.log(x)
calculates the natural logarithm (base \(e\)). If you want \(\log_{10}\) you can use math.log10
.
import math
math.log(32) # This is ln(32), not log₂(32)
3.4657359027997265