Download Lesson 12-3 notes: Arc Length, Area of a Sector, Radians

12-3 Sector Area and Arc Length
Objectives
Derive the formula for area of a circle
Find arc lengths and the area of sectors
using both degrees and radians.
Holt McDougal Geometry
12-3 Sector Area and Arc Length
Area of a Circle Proof
Workbook pg 503
Recall
The formula for circumference is C = 2r
The formula for area of a circle is A = r2
Holt McDougal Geometry
12-3 Sector Area and Arc Length
Example 1
The General Sherman tree in Sequoia
National Park, CA is considered the worlds
largest tree. The tree is approximately
circular at its base, with a circumference of
102.6ft. What is the approximate diameter
of the tree? What is the approximate area
of a cross section at the base? Round
each answer to the nearest foot.
Holt McDougal Geometry
12-3 Sector Area and Arc Length
• Turn to workbook page 504
• Highlight the definition of a sector and the
formula for area of a sector
• Complete example 2
Holt McDougal Geometry
12-3 Sector Area and Arc Length
In the same way that the area of a sector is a
fraction of the area of the circle, the length of an
arc is a fraction of the circumference of the circle.
• Highlight the definition of arc length and the
formula for arc length on workbook pg 505
• Complete example 3
Holt McDougal Geometry
12-3 Sector Area and Arc Length
Example 4
A windshield wiper blade is 18 inches long. To
the nearest square inch, what is the area
covered by the blade as it rotates through an
angle of 122°?
Holt McDougal Geometry
12-3 Sector Area and Arc Length
Degrees versus Radians
• Angles of a circle can be measured
in degrees out of 360o.
• Another unit used to measure
angles of a circle is radians.
• 2π radians = 360o = 1 full circle
• 1π = 180o = half a circle,
π/2 = 90o = ¼ a circle, etc
Holt McDougal Geometry
12-3 Sector Area and Arc Length
Example 5
Holt McDougal Geometry
12-3 Sector Area and Arc Length
Example 6
Calculate the arc length of each bolded arc in
radians.
A)
Holt McDougal Geometry
B)
12-3 Sector Area and Arc Length
Example 7
Calculate the area of each bolded sector in radians.
A)
Holt McDougal Geometry
B)
12-3 Sector Area and Arc Length
12-3 Assignments
• Primary assignment:
o Arc Length & Sector worksheet #1-23 odds
o Turn in the worksheet Monday 4/17
o Work must be shown for full credit
• Secondary Assignment:
o Arc Length & Sector worksheet #2–24 evens
Holt McDougal Geometry