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1 of 84 S HAPE AND S PACE Circles

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2 of 84 L ET US DEFINE C IRCLE A ___________is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center. A circle is a simple shape that is the set of all points in a plane that are at a given distance from a given point, the center.

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3 of 84 Radius is the distance from the center to the edge of a circle. Radius is half of the diameter

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4 of 84 Diameter is a segment that passes through the center and has its endpoints on the circle. The diameter is twice the length of the radius

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5 of 84 T HE VALUE OF We use the symbol π because the number cannot be written exactly. π = 3.141592653589793238462643383279502884197169 39937510582097494459230781640628620899862803482 53421170679821480865132823066470938446095505822 31725359408128481117450284102701938521105559644 62294895493038196 (to 200 decimal places)!

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6 of 84 In circles the AREA is equal to 3.14 ( ) times the radius (r) to the power of 2. Thus the formula looks like: A= r 2 In circles the circumference is formula looks like: 2 r The circumference of a circle is the actual length around the circle which is equal to 360°. π is equal to 3.14.

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7 of 84 T HE CIRCUMFERENCE OF A CIRCLE Use π = 3.14 to find the circumference of this circle. C = 2 πr 8 cm = 2 × 4 = 8 π R = 4

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8 of 84 T HE CIRCUMFERENCE OF A CIRCLE Use π = 3.14 to find the circumference of the following circles: C = 2 πr 4 cm = 2 × 2 = 4 π cm C = 2 πr 9 m = 2 × π × 9 = 18 π m C = 2 πr = 2 × 12 = 12 π mm C = 2 πr 58 cm = 2 × π × 58 = 116 π cm 24mm

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9 of 84 F ORMULA FOR THE AREA OF A CIRCLE We can find the area of a circle using the formula radius Area of a circle = πr 2 Area of a circle = π × r × r or

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10 of 84 A REA OF A CIRCLE

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11 of 84 T HE CIRCUMFERENCE OF A CIRCLE Use π = 3.14 to find the area of this circle. A = πr 2 4 cm = π × 4 × 4 = 16 π cm 2

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12 of 84 T HE AREA OF A CIRCLE Use π = 3.14 to find the area of the following circles: A = πr 2 2 cm = π × 2 2 = 4 π cm 2 A = πr 2 10 m = π × 5 2 = 25 π m 2 A = πr 2 23 mm = π × 23 2 = 529 π mm 2 A = πr 2 78 cm = π × 39 2 = 1521 π cm 2

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13 of 84 F IND THE AREA OF THIS SHAPE Use π = 3.14 to find area of this shape. The area of this shape is made up of the area of a circle of diameter 12cm and the area of a rectangle of width 6cm and length 12cm. 6 cm 12 cm Area of circle = π × 6 2 = 36 π cm 2 Area of rectangle = 6 × 12 = 78 cm 2 Total area = 36 π + 78

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14 of 84 ? F INDING THE RADIUS GIVEN THE CIRCUMFERENCE Use π = 3.14 to find the radius of this circle. C = 2 πr 12 cm How can we rearrange this to make r the subject of the formula? r = C 2π2π 12 2 × π = 6 π =

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15 of 84 F IND THE PERIMETER OF THIS SHAPE Use π = 3.14 to find perimeter of this shape. The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm. 6 cm 14 cm Perimeter = 14 x 6 Circumference = 2 πr

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16 of 84 C IRCUMFERENCE PROBLEM The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 1 km? 50 cm The circumference of the wheel = π × 50 Using C = 2 πr and π = 3.14, = 157 cm

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