The circumference of a circle is the distance all the way around its outer edge. It is like the perimeter of a polygon, but for a perfectly round shape. Circumference matters in real situations such as measuring wheels, circular tracks, pipes, gears, and round tables.
Once you know either the radius or the diameter, you can calculate the circumference using pi.
Key Facts
- Circumference means the distance around a circle.
- Diameter is twice the radius: d = 2r.
- Circumference using diameter: C = pi d.
- Circumference using radius: C = 2 pi r.
- Pi is the constant ratio of circumference to diameter: pi = C/d.
- For estimates, use pi ≈ 3.14 or pi ≈ 22/7 unless exact form is requested.
Vocabulary
- Circumference
- The circumference is the total distance around the outside of a circle.
- Radius
- The radius is the distance from the center of a circle to any point on the circle.
- Diameter
- The diameter is a line segment that passes through the center and connects two points on the circle.
- Pi
- Pi is the constant ratio of a circle's circumference to its diameter, approximately equal to 3.14.
- Center
- The center is the fixed point inside a circle that is the same distance from every point on the circle.
Common Mistakes to Avoid
- Using radius in C = pi d without doubling it first is wrong because the formula requires the diameter, not the radius.
- Forgetting units is wrong because circumference is a length, so the answer must use units such as cm, m, or in.
- Confusing area with circumference is wrong because area measures the space inside a circle while circumference measures the distance around it.
- Rounding pi too early is wrong because it can make the final answer less accurate, so keep more digits or use pi notation until the last step.
Practice Questions
- 1 A circular garden has a radius of 6 m. Find its circumference using pi ≈ 3.14.
- 2 A bicycle wheel has a diameter of 70 cm. How far does the bike travel in one full wheel rotation, using pi ≈ 3.14?
- 3 Two circles have radii 4 cm and 8 cm. Explain how their circumferences compare and why.