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. In Measurement, Circles, and 3D Solids, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Use radius and diameter
- Find circumference
- Find circle area
Worked example
Problem. A circle has radius 5. Find its area using pi = 3.14.
- Use A = pi r^2.
- A = 3.14 x 25.
- A = 78.5.
- Connect the result back to Circle Circumference and Area so the geometric relationship is explicit.
Answer: 78.5
Practice problems
1. A circle has radius 6. What is its diameter?
Show solution
- Warm-up: First identify exactly what the question is asking: A circle has radius 6. What is its diameter?
- For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
- Diameter is twice the radius.
- Check the result by substituting or estimating: the response should match 12 and make sense in the original problem.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
Answer: 12
2. A circle has diameter 18. What is its radius?
Show solution
- Warm-up: First identify exactly what the question is asking: A circle has diameter 18. What is its radius?
- For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
- Radius is half the diameter.
- Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
Answer: 9
3. Using pi = 3.14, find the circumference of a circle with diameter 10.
Show solution
- Core Practice: First identify exactly what the question is asking: Using pi = 3.14, find the circumference of a circle with diameter 10.
- For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
- C = pi d.
- Check the result by substituting or estimating: the response should match 31.4 and make sense in the original problem.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
Answer: 31.4
4. Using pi = 3.14, find the circumference of a circle with radius 4.
Show solution
- Core Practice: First identify exactly what the question is asking: Using pi = 3.14, find the circumference of a circle with radius 4.
- For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
- C = 2 pi r.
- Check the result by substituting or estimating: the response should match 25.12 and make sense in the original problem.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
Answer: 25.12
5. Using pi = 3.14, find the area of a circle with radius 7.
Show solution
- Challenge: First identify exactly what the question is asking: Using pi = 3.14, find the area of a circle with radius 7.
- For circle problems, connect the formula or theorem to the given radius, diameter, chord, arc, or center information.
- A = 3.14 x 49.
- Check the result by substituting or estimating: the response should match 153.86 and make sense in the original problem.
- Identify the diagram relationship, formula, theorem, or proof reason before calculating.
Answer: 153.86
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