Mrs. McConaughy Geometry 1

Any Way You Slice It: Any Way You Slice It: Calculating the Areas of Calculating the Areas of Circle PortionsCircle Portions

During this lesson, you will solve problems involving the areas of the following circle portions: sectors, segments, sectors, segments, and annuliand annuli.

Mrs. McConaughy Geometry 2

Before we start, recall:

RadiusRadius DiametDiameterer

CircumferenCircumferencece

AreaArea

5m5m

14 in.14 in.

18 18 ππ yd. yd.

121121ππ mm22

AREA (circle) = AREA (circle) = ππ r r22

Mrs. McConaughy Geometry 3

Before we start, recall:Before we start, recall:

AnnulusAnnulus- _______________________________________ region between two concentric circles

AREA AREA (annulus)(annulus) = = ππ R R2 2 - - ππ r r22

Mrs. McConaughy Geometry 4

SectorSector- ____________________________________________________________________

VOCABULARYVOCABULARY

region between an arc and two radii of a circle

AREA AREA (sector)(sector) = arc/360 = arc/360 ππ r r22

40

9 cm

Mrs. McConaughy Geometry 5

SegmentSegment- ___________________________________________________________________

VOCABULARYVOCABULARY

region between a chord and an arc of a circle

AREA AREA (segment)(segment) = Area = Area (sector)(sector) - Area - Area (triangle(triangle))

6 cm

Mrs. McConaughy Geometry 6

Final Checks for Final Checks for UnderstandingUnderstanding

1. Define and illustrate the following circle portions: sector, segment, and annulus.

2. Write formulas for the following circle portions: sector, segment, and annulus.

Mrs. McConaughy Geometry 7

HOMEWORK HOMEWORK ASSIGNMENT:ASSIGNMENT:

CIRCLE PORTIONS WSCIRCLE PORTIONS WS