Circumference Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Circumference.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The total distance around the outside of a circle; equal to \pi times the diameter or 2\pi r.
Imagine wrapping a string tightly around a circular jar lid, then straightening the string out. That length is the circumference. No matter the size of the circle, the circumference is always \pi times the diameter—roughly 3.14 laps of the diameter around the edge.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Circumference is the perimeter of a circle—it scales linearly with the radius.
Common stuck point: Remember: C = \pi d (using diameter) or C = 2\pi r (using radius). Don't confuse with area (\pi r^2).
Worked Examples
Example 1
easySolution
- 1 The circumference is the perimeter of a circle — the distance around it. Two equivalent formulas: C = 2\pi r (using radius) or C = \pi d (using diameter). They are equivalent since d = 2r.
- 2 Substitute r = 5 cm into C = 2\pi r: C = 2\pi(5) = 10\pi.
- 3 Result: C = 10\pi cm \approx 31.4 cm. The formula C = 2\pi r encodes the definition of \pi itself: \pi = C/d, the ratio of circumference to diameter, which is the same for every circle.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumBackground Knowledge
These ideas may be useful before you work through the harder examples.