Circles • Topic 2 of 3

Circumference of a Circle

What is circumference? The circumference of a circle is the total distance all the way around its outer edge. It is simply the special perimeter of a circle! If you took a piece of string, wrapped it perfectly around a tin can, and then laid the string flat against a ruler, the length you measure would be the circumference.

The Mystery of Pi ($\pi$): Thousands of years ago, mathematicians discovered a fascinating universal truth: if you take the circumference ($C$) of any circle ever made and divide it by its diameter ($d$), you always get the exact same number! This unchanging ratio is a mathematical constant named Pi, written with the Greek symbol $\pi$.

Because $\pi$ is an irrational number, its decimal digits keep going forever without repeating ($3.14159...$). For school geometry calculations, we use two very close approximations:

As a decimal: $\pi \approx 3.14$
As a fraction: $\pi \approx \frac{22}{7}$

Circumference Formulas: By rearranging the definition of Pi ($\frac{C}{d} = \pi$), we get our perimeter formulas:

Using diameter: $C = \pi d$
Using radius (since $d = 2r$): $C = 2\pi r$

Solved Examples

Worked Example

Find the circumference of a circular plate whose radius is $7\text{ cm}$. (Use $\pi = \frac{22}{7}$)

Solution*Step 1: Note the given dimensions:* $r = 7\text{ cm}$ *Step 2: Select the appropriate circumference formula that matches a radius:* $C = 2\pi r$ *Step 3: Substitute the known values into the equation:* $C = 2 \times \frac{22}{7} \times 7$ *Step 4: Simplify by canceling out the common $7$ in the numerator and denominator:* $C = 2 \times 22 \times 1$ *Step 5: Perform the final multiplication:* $C = 44\text{ cm}$

Key Points

Circumference is the linear perimeter length all the way around a circle.
Pi ($\pi$) is the constant ratio of circumference divided by diameter ($\pi = \frac{C}{d}$).
The common numerical fraction values used for $\pi$ are $\frac{22}{7}$ or $3.14$.
The two core mathematical formulas are $C = \pi d$ and $C = 2\pi r$.
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Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The circumference of a circle is:

Explanation: $2\pi r$.

Q2.The circumference can also be written as:

Explanation: $C=\pi d$.

Q3.For $r=7$ (using $\pi=\tfrac{22}{7}$), $C=$

Explanation: $2\cdot\tfrac{22}{7}\cdot7=44$.

Q4.$\pi$ is approximately:

Explanation: $\approx3.14$ or $\tfrac{22}{7}$.

Practice more MCQs → 📝 Assignment · 35 marks