Arc Length and Area of Sectors
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Sectors are portions of circles used to describe parts of pie charts, computer hard drives, traffic interchanges, and pizza. The document defines minor and major sectors and explains how to calculate the length of arc and area of sectors using fractions of the full circle and formulas involving radius and circumference or area. Sample calculations are shown for a minor 60 degree sector and a major 300 degree sector of a circle with a radius of 10 cm.
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This document defines key terms and concepts related to circles, including:
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Circles (2)
This document defines key terms and concepts related to circles, including:
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Circles(1)
The document provides information about calculating geometric properties of circles such as circumference, area, perimeter and area of sectors, as well as the volumes of cylinders. It includes formulas, examples of calculations, and multiple choice questions to test understanding. Key formulas covered include circumference = π x diameter, area of a circle = π x radius^2, area of a sector = (angle of sector/360) x π x radius^2, and volume of a cylinder = area of base x height. The document provides a review of foundational circle geometry concepts through examples, practice questions, and matching definitions to geometric terms.
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Circle
CIRCLE
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A circle can be defined in two ways.
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Arc Length and Area of Sectors
- 2. Pie charts are divided up into fractions of the full circle. In Maths, each division is called a “Sector”.
- 3. “Clover Leaf” interchanges on Freeways contain four “sectors”, eg. they are not quite full circles.
- 4. Computer hard drives store information in areas called “sectors” that are a little different to the “sectors” we are doing.
- 5. Sectors can be shaped like pieces of Pie (minor sectors), or Pacman shape (Major sectors). Quarter and Half Circles are also “Sectors”.
- 6. Cutting up a Pizza creates fractions of a circle called “Sectors”.
- 7. 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 of the full 360 o of the circle. L = 60 / 360 of a full circle This 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
- 8. 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 circle the full 360 o of the circle. L = 300/360 x ( Ԉ R x 2 ) x This fraction is 300 / 360 L = 0.8333 x ( 3.1416 x 10 x 2 ) The large remaining part of this circle is called a “MAJOR Sector”. L = 52.4 cm
- 11. 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 of the full 360 o of the circle. A = 60 / 360 of a full circle This 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
- 12. 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 circle the full 360 o of the circle. A = 300/360 x ( Ԉ R2 ) x This fraction is 300 / 360 A = 0.8333 x ( 3.1416 x 10 x 10 ) The large remaining part of the circle is called a “MAJOR Sector”. A = 262 cm2
- 16. http://passyworldofmathematics.com/ All slides are exclusive Copyright of Passy’s World of Mathematics Visit our site for Free Mathematics PowerPoints