11.4: Circumference and Arc Length

Objectives:• Develop and apply the equation for the circumference of a circle• Determine arc length of a circle

Common core standards:• A-SSE-1, G-CO-1, G-C-5, G-MG-1, N-Q-1

A circle is the locus of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol and its center. A has radius r = AB and diameter d = CD.

Solving for C gives the formulaC = d. Also d = 2r, so C = 2r.

The irrational number is defined as the ratio ofthe circumference C tothe diameter d, or

EXAMPLE 1Find the indicated measures.

The exact circumference of a circle with radius 9 centimeters

The exact radius of a circle with circumference 26 meters

EXAMPLE 2

The dimensions of a car tire are shown at the right. To the nearest foot, how far does the tire travel when it makes 15 revolutions?

Tire Revolutions

GUIDED PRACTICE Find the circumference of a circle with diameter 5 inches.

Find the diameter of a circle with circumference 17 feet.

EXAMPLE 3Find the length of each red arc.

Find the indicated measure.

Circumference C of Z

EXAMPLE 4Find the indicated measure.

m RS

GUIDED PRACTICEFind the indicated measure.

Length of PQ

9 is the diameter

GUIDED PRACTICE

Circumference of N

Find the indicated measure.

GUIDED PRACTICE

Radius of G

Find the indicated measure.