Lesson 11.2.1

Circumference of Circles

The circumference is the distance around a circle: .

Introduction

Past Knowledge

Circle vocab (10.1.1). d = 2r. Pi ≈ 3.14159.

Today's Goal

Compute circumference using C = 2πr or C = πd.

Future Success

Arc length (11.2.2), area of circles (11.2.3).

Key Concepts

Circumference Formulas

is the ratio of circumference to diameter — constant for ALL circles.

Exact vs. Approximate

Leave answers in terms of for exact answers (e.g., cm). Use only when asked to approximate.

Derivation

By definition, . Solving for C:

∎ Pi literally IS the circumference-to-diameter ratio.

Worked Examples

Basic

Given Radius

r = 7 cm

C = 14π ≈ 44.0 cm

Intermediate

Find Radius from C

C = 50 in. Find r.

→ in

r ≈ 7.96 in

Common Pitfalls

Radius vs. Diameter

C = 2πr OR C = πd. If given diameter, don't double it again.

Real-Life Applications

Tires & Odometers

An odometer counts tire rotations. Distance = circumference × rotations.

Fencing Circular Gardens

The amount of fencing around a circular flower bed = circumference.