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Circle Circumference and Area

A free Geometry lesson from the “Measurement, Circles, and 3D Solids” unit, with a worked example and practice problems including step-by-step solutions.

The radius goes from the center to the circle, and the diameter is twice the radius. Circumference is distance around a circle, and area is the space inside.

What you'll learn

Why it matters: Mechanics, designers, and athletes use circumference and area for wheels, tracks, gears, and round fields.

Worked example

Problem. A circle has radius 5. Find its area using pi = 3.14.

  1. Use A = pi r^2.
  2. A = 3.14 x 25.
  3. A = 78.5.

Answer: 78.5

Practice problems

1. A circle has radius 6. What is its diameter?

Show solution
  1. Warm-up: First identify exactly what the question is asking: A circle has radius 6. What is its diameter?
  2. For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
  3. Diameter is twice the radius.
  4. Check the result by substituting or estimating: the response should match 12 and make sense in the original problem.

Answer: 12

2. A circle has diameter 18. What is its radius?

Show solution
  1. Warm-up: First identify exactly what the question is asking: A circle has diameter 18. What is its radius?
  2. For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
  3. Radius is half the diameter.
  4. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

3. Using pi = 3.14, find the circumference of a circle with diameter 10.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Using pi = 3.14, find the circumference of a circle with diameter 10.
  2. For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
  3. C = pi d.
  4. Check the result by substituting or estimating: the response should match 31.4 and make sense in the original problem.

Answer: 31.4

4. Using pi = 3.14, find the circumference of a circle with radius 4.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Using pi = 3.14, find the circumference of a circle with radius 4.
  2. For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
  3. C = 2 pi r.
  4. Check the result by substituting or estimating: the response should match 25.12 and make sense in the original problem.

Answer: 25.12

5. Using pi = 3.14, find the area of a circle with radius 7.

Show solution
  1. Challenge: First identify exactly what the question is asking: Using pi = 3.14, find the area of a circle with radius 7.
  2. For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
  3. A = 3.14 x 49.
  4. Check the result by substituting or estimating: the response should match 153.86 and make sense in the original problem.

Answer: 153.86

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