Page 103 - IM_FL_Geometry_Print Sample

2. What is the radian measure of the central angle that traces out the entire circle?
3. Find the radian measure of a central angle that traces out each fraction of a circle. Include a sketch of each.
a. of a circle. b. of a circle. c. of a circle.
d. of a circle.
4. A circle has a circumference of 50 inches and a central angle that traces out an arc length of 14 inches. What is the radian measure of the central angle? Include a sketch of the circle in your response.
5. A circle has a central angle measure of radians and a circumference of 5 meters.
What is the arc length traced out by the central angle? Include a sketch of the circle in your response.
Student Response
1. 2. 3.
4. 5.
units. radians.
a. radians. b. radians.
c. radians. d. radians.
radians, or approximately 1.76 radians. The sketch should show a central angle that is approximately of the circle.
meters. The sketch should show a central angle that a third of the circle.
Activity Synthesis
The key idea to come away with is that radian measures range from 0 to . Display student sketches to illustrate that radians range from 0 to . Ask previously identi ed students to share their responses to question 5 and to explain how they decided to sketch the central angle. Focus on these two strategies for nding arc length:
• Calculating the fraction of the circle that the arc traces and then multiplying the circumference by that fraction.
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Teacher Guide