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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

Why it matters: Pizza sizing (area), bike tire revolutions (circumference), sprinkler coverage, and circular tabletops all rely on these two formulas.

Worked example

Problem. A circle has radius 5. Use pi = 3.14 to find its circumference and area.

  1. C = 2 * pi * r = 2 * 3.14 * 5 = 31.4.
  2. A = pi * r^2 = 3.14 * 25 = 78.5.
  3. Connect the calculation back to Circles: Circumference and Area so the method, not just the arithmetic, is clear.
  4. Check the result against the original question before writing the final answer.

Answer: C = 31.4, A = 78.5

Practice problems

1. Circumference with r = 10 (pi = 3.14).

Show solution
  1. Warm-up: First identify exactly what the question is asking: Circumference with r = 10 (pi = 3.14).
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. C = 2 * 3.14 * 10.
  4. = 62.8.
  5. Check the result by substituting or estimating: the response should match 62.8 and make sense in the original problem.

Answer: 62.8

2. Circumference with d = 8 (pi = 3.14).

Show solution
  1. Warm-up: First identify exactly what the question is asking: Circumference with d = 8 (pi = 3.14).
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. C = pi * d = 3.14 * 8.
  4. = 25.12.
  5. Check the result by substituting or estimating: the response should match 25.12 and make sense in the original problem.

Answer: 25.12

3. Area with r = 6 (pi = 3.14).

Show solution
  1. Warm-up: First identify exactly what the question is asking: Area with r = 6 (pi = 3.14).
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. A = 3.14 * 36.
  4. = 113.04.
  5. Check the result by substituting or estimating: the response should match 113.04 and make sense in the original problem.

Answer: 113.04

4. Area with r = 10 (pi = 3.14).

Show solution
  1. Core Practice: First identify exactly what the question is asking: Area with r = 10 (pi = 3.14).
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. A = 3.14 * 100.
  4. = 314.
  5. Check the result by substituting or estimating: the response should match 314 and make sense in the original problem.

Answer: 314

5. Circumference with r = 7 (pi = 3.14).

Show solution
  1. Core Practice: First identify exactly what the question is asking: Circumference with r = 7 (pi = 3.14).
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. C = 2 * 3.14 * 7.
  4. = 43.96.
  5. Check the result by substituting or estimating: the response should match 43.96 and make sense in the original problem.

Answer: 43.96

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