Circles: Circumference and Area
A free Pre-Algebra lesson from the “Geometry Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Every circle has a radius r (center to edge) and a diameter d = 2r. The distance around is the circumference: C = 2 * pi * r = pi * d. The space inside is the area: A = pi * r^2. Use pi = 3.14 (or 22/7) for arithmetic answers. In Geometry Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Apply C = 2 * pi * r or pi * d to find circumference
- Apply A = pi * r^2 to find the area of a circle
- Solve real-world circle problems using pi = 3.14
Worked example
Problem. A circle has radius 5. Use pi = 3.14 to find its circumference and area.
- C = 2 * pi * r = 2 * 3.14 * 5 = 31.4.
- A = pi * r^2 = 3.14 * 25 = 78.5.
- Connect the calculation back to Circles: Circumference and Area so the method, not just the arithmetic, is clear.
- Check the result against the original question before writing the final answer.
Answer: C = 31.4, A = 78.5
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response). Counts include repeated prompts and variants.
Practice problems
1. Circumference with r = 10 (pi = 3.14).
Show solution
- C = 2 * 3.14 * 10.
- = 62.8.
Answer: 62.8
2. Circumference with d = 8 (pi = 3.14).
Show solution
- C = pi * d = 3.14 * 8.
- = 25.12.
Answer: 25.12
3. Area with r = 6 (pi = 3.14).
Show solution
- A = 3.14 * 36.
- = 113.04.
Answer: 113.04
4. Area with r = 10 (pi = 3.14).
Show solution
- A = 3.14 * 100.
- = 314.
Answer: 314
5. Circumference with r = 7 (pi = 3.14).
Show solution
- C = 2 * 3.14 * 7.
- = 43.96.
Answer: 43.96
Practice this interactively with instant feedback and an AI tutor.
Practice Circles: Circumference and Area Take the free placement check