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11 5 circumfrence and area of a circle lessonPresentation Transcript
Circumference of a CircleCircumference of a CircleYou will learn to solve problems involving circumferences ofcirlces.1) circumference2) pi (π)
Circumference of a CircleCircumference of a CircleAn in-line skate advertises “80-mm clear wheels.”The description “80-mm” refers to the diameter of the skates’ wheels.As the wheels of an in-line skate complete one revolution, thedistance traveled is the same as the circumference of the wheel.Just as the perimeter of a polygon is the distance around the polygon,the circumference of a circle is the ______________________.distance around the circle
Circumference of a CircleCircumference of a CircleGo to this website to Analyze your Data.Go to this website to Collect Data from various Circles.On a sheet of paper, create a table similar to the one below:Circumference DiameterRatio:C/DResult271 86 271 ÷ 86 3.151163Example Data
Circumference of a CircleCircumference of a CircleIn the previous activity, the ratio of the circumference C of a circle to itsdiameter d appears to be a fixed number slightly greater than 3, regardlessof the size of the circle.The ratio of the circumference of a circle to its diameter is always fixed andequals an irrational number called __ or __.pi πThus, ____ = __,Cdπ or C=πd .Since d = 2r, the relationship can also be written as C=2πr.
Circumference of a CircleCircumference of a CircleTheorem11-7Circumferenceof a CircleIf a circle has a circumference of C units and a radius of runits, then C = ____2πr or C = ___πdCdr
Area of a CircleArea of a CircleYou will learn to solve problems involving areas and sectorsof circles.1) sector
Area of a CircleArea of a CircleThe space enclosed inside a circle is its area.By slicing a circle into equal pie-shaped pieces as shown below, you canrearrange the pieces into an approximate rectangle.Note that the length along the top and bottom of this rectangle equals the_____________ of the circle, ____.circumference 2πrSo, each “length” of this approximate rectangle is half the circumference,or __πr
Area of a CircleArea of a CircleThe “width” of the approximate rectangle is the radius r of the circle.Recall that the area of a rectangle is the product of its length and width.Therefore, the area of this approximate rectangle is (π r)r or ___.πr2
Area of a CircleArea of a CircleTheorem11-8Areaof a CircleIf a circle has an area of A square units and a radius ofr units, then A = ___πr2A=πr2r
Area of a CircleArea of a CircleFind the area of the circle whose circumference is 6.28 meters.Round to the nearest hundredth.A=πr2You could calculate thearea if you only knewthe radius.Any ideas?C=2πrUse your knowledgeof circumference.Solve for radius, r.C2π=r1=rA=π(1)2A=πA=3.14m26.282π=r
Area of a CircleArea of a CircleTheorem 11-9Area of aSector of aCircleIf a sector of a circle has an area of A square units, acentral angle measurement of N degrees, and a radius ofr units, thenA=N360(π r2)