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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.

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.

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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