Central Angles and Arcs
Circumference of a Circle:
Central Angles :
Proportion relating central angles and arcs
!
s
=
360 C
Example 1: In a circle with circumference 72 inches, find the measure of the central
angle, ! , that is intercepted by an arc with a length of 12 inches.
Example 2: How large an arc is intercepted by a central angle of 6.23° on a circle with a
radius of 10 cm ?
Example 3: In a circle, the central angle of 40° intercepts an arc that measures 55 cm.
Find the radius of the circle.
Example 4: In a circle, the central angle of 10°15’32” intercepts an arc that measures
55 cm. Find the circumference of the circle.
Central Angles and Arcs
Activity: Materials: Styrofoam balls with a wedge cut out and Sharpie Markers.
1.) Students identify the equator on their Styrofoam ball with a sharpie.
2.) Students identify the center of the Earth on their Styrofoam ball with a
sharpie.
3.) Students draw one line of longitude on the edge of where the wedge was cut.
4.) Students plot San Francisco and Seattle on the line of longitude.
5.) Students draw angles for the lines of latitude.
Find the distance between the cities of San Francisco and Seattle using the
proportion relating Central Angles and Arcs: