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Published byFrederica Perry Modified over 6 years ago

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Area of a Circle π

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Starter Which of these shapes has the greatest perimeter? Which has the smallest? What is each perimeter in terms of d? d d d

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Starter Answer Square has 4 sides of length d 4d Hexagon has 6 sides of ½d3d d d d ½d

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Starter Answer Square has 4 sides of length d 4d Hexagon has 6 sides of ½d3d Circle is between 3d and 4dπd

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Areas Which of these shapes has the greatest area? Which has the smallest? What is the area in terms of r? rrr

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Areas Large square is 2r x 2r = 4r 2 Small square is half of this = 2r 2 rrr 2r

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Areas Large square is 2r x 2r = 4r 2 Small square is half of this = 2r 2 Circle has area in between 2r 2 and 4r 2

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Area of a circle A circle has radius r

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Rearrange the sectors

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Consider the lengths Circumference of circle = 2πr Length of half circumference = πr So the length of this side is πr

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Consider the lengths Radius of circle = r So the height is r πrπr

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Consider the area Area of shape is close to area of parallelogram = base x height = πr x r = πr 2 r πrπr Hence the area of a circle is = πr 2

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Summary A circle has radius r and diameter d Circumference of a circle C = π d or C = 2 π r Area of a circle A = π r 2 r d Fiddle-dee-dum, fiddle-dee-dee A ring round the moon is π times d But if you want a hole repaired Then what you need is πr 2.

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