Areas of Circles and Sectors

Sec. 7 – 7 Areas of Circles & Sectors Objective: To find the areas of circles, sectors and segments of circles

Area of a Circle r r A =  r 2 Pi = 3.14 = 22/7 Radius of Circle r

Example1: How much more pizza is in a 12in diameter pizza than in a 10in diameter pizza? A 12 =  r 2 = 6 2  = 36  = 113.1in 2 A 10 =  r 2 =5 2  = 25  = 78.5in 2 36  - 25  = 11  = 34.6in 2

[object Object],[object Object],[object Object],[object Object],C P D A = mARC 360  r 2 Area of sector Fraction of Circle Area of Circle P

Example 2: Find the area of sector ABS 100  6cm A sector = mAS 360  r 2 = 100/360 • (6 2 )  = .278 • (36  ) = 31.4cm 2 B A S

[object Object],Area of a Δ A = ½ bh Area of the Segment A segment = A sector - A Δ

Example 3: Find the area of the segment m  ABC = 90 ° C B A 45 45 A segment = A sector CBA – A Δ CBA = (mCA)360 •  r 2 - ½bh = (90)/360 •  (10) 2 - ½(14.2)(7.1) = 78.5 – 50.4 = 28.1cm 2 10cm 45 = 10/ √2 =7.1

What have we learned?? ,[object Object],[object Object],[object Object],A = mARC 360  r 2 A segment = A sector - A Δ A =  r 2 A =  r 2

Areas of Circles and Sectors

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