12 3 Sector Area and Arc Length Objectives

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 Mc. Dougal 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 = r 2 Holt Mc. Dougal 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. 6 ft. 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 Mc. Dougal 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 Mc. Dougal 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 pg 505 example 3 Holt Mc. Dougal 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 Mc. Dougal Geometry

12 -3 Sector Area and Arc Length Degrees versus Radians • Angles of a circle can be measured in degrees out of 360 o. • Another unit used to measure angles of a circle is radians. • 2π radians = 360 o = 1 full circle • 1π = 180 o = half a circle π/2 = 90 o = ¼ a circle … Holt Mc. Dougal Geometry

12 -3 Sector Area and Arc Length Example 5 Holt Mc. Dougal Geometry

12 -3 Sector Area and Arc Length Example 6 Calculate the arc length of each bolded arc. Do not round. A) Holt Mc. Dougal Geometry B)

12 -3 Sector Area and Arc Length Example 7 Calculate the area of each bolded sector do not round. A) Holt Mc. Dougal Geometry B)

12 -3 Sector Area and Arc Length 12 -3 Assignments • Primary assignment: o Arc Length & Sector worksheet #1 -23 odds o Periods 1, 5, & 7 due Monday 4/23 o Periods 2, 4, & 6 due Tuesday 4/24 o Work must be shown for full credit • Secondary Assignment: o Arc Length & Sector worksheet #2– 24 evens Holt Mc. Dougal Geometry