Circumference
In short: Circumference is the length of the boundary of a circle, computed by multiplying the diameter by pi or, in other words, multiplying twice the radius by pi.
7th GradeGeometry7.G.B.4
What is Circumference?
Stroll once along the edge of a round fountain and the length of your stroll is its circumference. For a circle it does the job that perimeter does for a polygon.
Two formulas produce it: \(C = \pi d\) and \(C = 2\pi r\). They agree because \(d = 2r\). Since \(\pi\) is about 3.14159, the trip around any circle runs a little over three times the trip across. The result is a length, so it carries units such as inches or meters.
How to spot it
- You are asked how far a wheel rolls in one turn, or how much ribbon wraps around a round can.
- A radius or diameter is given and the target is the length of the boundary.
- The wording mentions a running track, a circular garden border or a hoop.
- A boundary length is known and you must work backward to the width.
The method
- Write down the diameter, or double the radius to produce it.
- Multiply by \(\pi\): use 3.14 for a rough estimate or the pi key for more digits.
- Round only at the very end and attach a length unit.
- Working backward, divide the circumference by \(\pi\) to recover the diameter.
Circumference: solved example
Problem
A circus unicycle wheel measures 26 inches across. How much ground does the rider cover during one complete revolution of the wheel?
Solution
One revolution covers one circumference: \(C = \pi d = 26\pi\).
With \(\pi \approx 3.14159\), \(C \approx 81.68\). The rider advances about 81.68 inches, roughly 6.8 feet, each turn.
Try it
Question 1
A dollhouse table top has a radius of 6.5 centimeters. Find the length of its edge.
Show the answer
\(C = 2\pi r = 13\pi \approx 40.84\) centimeters.
Question 2
A circular jogging loop is 94.2 feet around. Taking \(\pi\) as 3.14, how wide is the loop?
Show the answer
\(d = \frac{94.2}{3.14} = 30\) feet.
Circumference vs. Area of a Circle
Circumference gauges a length along the edge and comes in plain units like inches. Area gauges the flat space inside and comes in square units. Double the radius and the edge length doubles, but the area becomes four times as large, so the two quantities grow at different speeds.
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Whole dictionary: A–Z · 7th Grade · Geometry