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Circumference of a Circle
Geometry • Grades 5, 6, 7, 8
Geometry
Circumference of a Circle
Calculate the distance around any circle.
The Formula
C = 2πr
Used for: Finding the perimeter (distance around) a circle
CCircumference / perimeter length
πPi constant ≈ 3.14159265...
rRadius of the circle
dDiameter (2r)
⚡Live Interactive Quick Solver
Instant Calculationunits (d = 10)
Circumference (C):31.42 units
Exact form: 10π• Step: C = 2 × π × 5 = 31.42
C = 2\pi r = \pi d
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🎯 Key Concepts
Two ways to calculate circumference:
📏
C = πd (using diameter)Alternative form when diameter is given
🔄
d = 2rDiameter is twice the radius
📐
C = 2πr or πdBoth formulas give the same result
📝 Worked Examples
Example 1: Given Radius
Problem:
Find circumference if radius = 7 cm1
Write formula
C = 2πr2
Substitute
C = 2 × π × 73
Calculate
C = 14π ≈ 43.98 cmAnswer: C ≈ 43.98 cm
Example 2: Given Diameter
Problem:
Find circumference if diameter = 10 cm1
Use diameter formula
C = πd2
Substitute
C = π × 103
Calculate
C = 10π ≈ 31.42 cmAnswer: C ≈ 31.42 cm
Example 3: Finding Radius
Problem:
Circumference is 62.8 cm. Find radius.1
Rearrange formula
r = C / 2π2
Substitute
r = 62.8 / (2 × 3.14)3
Calculate
r = 62.8 / 6.28 = 10 cmAnswer: r = 10 cm
💡 Pro Tips
π is the ratio
For any circle, circumference ÷ diameter = π (always!)
Double radius = double C
Unlike area (which quadruples), circumference just doubles!
Quick check
Circumference is about 3× the diameter
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