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# Arc Length and Area of Sectors

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Sectors of Circles - Length and Area

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### Arc Length and Area of Sectors

1. 1. Pie charts are divided up intofractions of the full circle. In Maths, each division is called a “Sector”.
2. 2. “Clover Leaf” interchanges onFreeways contain four “sectors”,eg. they are not quite full circles.
3. 3. Computer hard drives store informationin areas called “sectors” that are a littledifferent to the “sectors” we are doing.
4. 4. Sectors can be shaped like pieces of Pie (minor sectors), or Pacman shape (Major sectors). Quarter and Half Circles are also “Sectors”.
5. 5. Cutting up a Pizza creates fractions of a circle called “Sectors”.
6. 6. L = Length of Arc around Pizza Edge L 360 o 60 o R = 10 cm All the way around a Circle is the “Circumference” of C = Ԉ R x 2 where Ԉ 3.1416 x =We only have 60 o out ofthe full 360 o of the circle. L = 60 / 360 of a full circleThis fraction is 60 / 360 L = 60/360 x ( Ԉ R x 2 ) x L = 0.1667 x ( 3.1416 x 10 x 2 )This small piece of pizza part of the circle is called a “Minor Sector”. L = 10.5 cm
7. 7. L = Length of Arc around Pizza 360 o 300 o All the way around a Circle is the “Circumference” of R = 10 cm C = Ԉ R x 2 where Ԉ 3.1416 x =We only have 300 o out of L = 300 / 360 of a full circlethe full 360 o of the circle. L = 300/360 x ( Ԉ R x 2 ) xThis fraction is 300 / 360 L = 0.8333 x ( 3.1416 x 10 x 2 ) The large remaining part of thiscircle is called a “MAJOR Sector”. L = 52.4 cm
8. 8. A = Area of one piece of Pizza 360 o 60 o R = 10 cm The full AREA inside a Circle is given by the formula: A = Ԉ R2 where Ԉ 3.1416 x =We only have 60 o out ofthe full 360 o of the circle. A = 60 / 360 of a full circleThis fraction is 60 / 360 A = 60/360 x ( Ԉ R x R ) x A = 0.1667 x ( 3.1416 x 10 x 10 )This small piece of pizza part of the circle is called a “Minor Sector”. A = 52.3 cm2
9. 9. A = Area of Remaining Pizza 360 o 300 o The full AREA inside a Circle is given by the formula: R = 10 cm A = Ԉ R2 where Ԉ 3.1416 x =We only have 300 o out of We have 300 / 360 of the full circlethe full 360 o of the circle. A = 300/360 x ( Ԉ R2 ) xThis fraction is 300 / 360 A = 0.8333 x ( 3.1416 x 10 x 10 ) The large remaining part of thecircle is called a “MAJOR Sector”. A = 262 cm2