5-7 Circles:

Circumference and Arc Length

Objective:  Find the circumference of a circle and the length of an arc.

pi (π) = ratio of circumference of a circle to its diameter

π     3.14      22/7

Circumference (Perimeter)Theorem 5-10

The circumference of a circle is π times the diameter.

Example:

Find the circumference of a circle with a diameter of 16 cm.

concentric circles:  two circles that lie in the same plane and have the same center

Example:  The radii of two concentric circles is 2:1, what is the ratio of their circumferences?

Arc length:  the distance along an arc measured in linear units ( ft, m, yds, etc.)

** The length of an arc is a fraction of the circumference of the circle.

Example:  An arc of 90° represents 90/360 or 1/4 of the circle, so its arc length is 1/4 the circumference of the circle.

THEOREM 5­11

Example:Find the arc length. Give answers in terms of π and rounded to the 

nearest hundredth.

120°

You Try:Find the arc length. Give your 

answer in terms of π and rounded to the nearest hundredth.

Congruent arcs:arcs that have the same measure and are in the same circle or in congruent circles

Arc Length # 1Find the lengths to the nearest tenth

AND in terms of π.

HW # 55: p. 282-283# 9-13, 19-22