DoAssignment study guide
E2.3 · Connect radius, diameter, and circumference
Learn to connect radius, diameter, and circumference through clear examples and targeted practice.
Ontario Grade 7 Mathematics
Spatial Sense
Measure around a circle
A radius runs from the centre of a circle to its edge. A diameter goes across the centre from one edge to the other, so it is two radii long. Circumference is the distance all the way around the edge. For every circle, circumference divided by diameter is the constant pi, written π. The diagram below is a labelled schematic: it identifies the parts, while its screen pixels do not set a physical scale.
What you will learn
- Identify radius, diameter, and circumference.
- Use diameter = 2 × radius.
- Find circumference with π × diameter and include units.
Name the lengths
If a radius is 4 cm, the diameter is 8 cm. Both are straight-line distances. The circumference follows the curved boundary, so it is longer than the diameter. Do not confuse the area inside the circle with the distance around it.
Use the constant ratio
For any circle, circumference ÷ diameter is π. Therefore circumference = π × diameter, or equivalently 2 × π × radius. Keep π in an exact answer when possible; use 3.14 only for an approximation.
Check a result
The circumference should be a little more than three diameters. With diameter 8 cm, 8π cm is about 25.13 cm. A result of 8 square centimetres would use the wrong quantity and the wrong unit.
Worked example
A circle with radius four centimetres
A circular badge has radius 4 cm. Find its diameter and circumference.
The orange segment runs from centre to edge and represents a radius of 4 cm. The diameter is twice that distance; the circular boundary is the circumference.
- Double the radiusDiameter = 2 × 4 = 8 cm.
- Use the circumference relationCircumference = π × diameter = 8π cm.
- EstimateUsing π ≈ 3.14 gives about 25.12 cm, slightly more than three diameters.
Answer: Diameter is 8 cm; circumference is exactly 8π cm, approximately 25.12 cm.
Check: 25.12 ÷ 8 ≈ 3.14, consistent with π.
Common mistakes and how to avoid them
Using radius 4 cm as though it were the diameter.
Correction: A diameter crosses the whole circle through its centre. Double the radius first.
Lesson summary
- Radius goes from centre to edge.
- Diameter equals twice the radius.
- Circumference is the edge length, equal to π times the diameter.
Check your understanding
Question 1
A circle has diameter 10 cm. What is its exact circumference?
- 10π cm
- 5π cm
- 20π cm
- 100π cm
Show answer and explanation
10π cm
Circumference = π × diameter = 10π cm.
Key terms
- Radius
- Distance from a circle’s centre to its boundary.
- Circumference
- Distance along the entire boundary of a circle.
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About this lesson and its review
Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation E2.3. It is a study resource, not an official curriculum publication.
Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.