Arc Lengths and Areas of Sectors Lesson 11.6 Geometry Honors

1
Arc Lengths and Areas of SectorsLesson
11.6Geometry Honors

• Objective Know and use the formulas for Arc
  Lengths and Areas of Sectors.

2
Lesson Focus

• This lesson shows how the length of an arc of a
  circle and the area of a region or sector of a
  circle can be calculated.

3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
Basic Terms

• Sector of a Circle
• A region bounded by two radii and an arc of the
  circle.

12
Arc Length
13
Arc Length
If the measure of minor arc AB x, then the
length of minor arc AB (x/360)(2pr)
Do not confuse arc measure with arc length. Arc
measure equals the measure of the corresponding
central angel and is independent of the size of
the circle. Arc length depends on the size of
the circle because it is a part of the
circumference of the circle.
14
Area of a Sector
15
Area of a Sector
If the measure of minor arc AB x, then the
area of sector AOB (x/360)(pr2)
Except for special cases, finding the area of a
region bounded by a chord and its arc usually
requires the use of trigonometry.
16
Practice

• The radius of a circle is 3 cm.
• Find (a) the lengths of the given arcs, and
• (b) the areas of the sectors determined by
  the given arcs.
• 50
• 20
• 140

17
Written Exercises

• Problem Set 11.6, p.453 2 14 (even)
• Handout 11-6