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Geometry 11.5 Circumference and Area of Circles

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Let’s talk about Pi……… Pi is the ratio of the circumference of a circle to its diameter. The symbol for pi is π This ratio is the same for all circles. d π = C d

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PI 3. 141592653589793238462643383279502884197169399375105820974944 592307816406286208998628034825342117067982148086513282306647 093844609550582231725359408128481117450284102701938521105559 644622948954930381964428810975665933446128475648233786783165 271201909145648566923460348610454326648213393607260249141273 724587006606315588174881520920962829254091715364367892590360 011330530548820466521384146951941511609433057270365759591953 092186117381932611793105118548074462379962749567351885752724 891227938183011949129833673362440656643086021394946395224737 190702179860943702770539217176293176752384674818467669405132 000568127145263560827785771342757789609173637178721468440901 224953430146549585371050792279689258923542019956112129021960 864034418159813629774771309960518707211349999998372978049951 …and so on, never terminating, never repeating……. Pi is an IRRATIONAL NUMBER The Value of Pi………

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Approximate Value of Pi……… π ≈ Usually in this class, we will leave pi as a constant. For example, we may say that the area of a circle is 5π, or 6aπ, or 12.6π, etc. The π symbol will remain in our expression. When you need to use a decimal approximation of pi: π ≈ 3.14 When you need to use a fractional approximation of pi: 22 7

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Circle Formulas Area = πr² r d Circumference = 2πr = d π

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Exercises 1. A = π(5)² = 25π 2. r = ½(12) = 6 A = π(6)² = 36π 3. r = √16 = 4 C = 2(4)π = 8π 4. A = π(8)² = 64π C = dπ = 16π 5 C = dπ = 10π C = 12π 6 A = 16π 4 r = 8 8

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Exercises 5. r = ½(100) = 50 6. r = √121 = 11 C = 2(11)π = 22π A = π(50)² = 2500π C = 100π 50 A = 121π 11

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Exercises 7. A = πr² Find the diameter of a pipe if the area of a cross-section is 50.24 cm 2 (Use 3.14 for pi Find the radius of a pizza pan if its circumference is 12.56 ft. (Use 3.14 for pi) 50.24 = 3.14r² r² = 16 r = 4 d = 8 8. C = dπ 12.56 = 3.14d d = 4 r = 2

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Exercises Nick wants to enclose his brand new GEO in a circular fence that costs $2.95/ft. If the circle has a radius of 3.5 ft., how much will the fencing cost? (use 22/7 for π.) We need to find Circumference: C = 2(3.5)(22/7) C = 7(22/7) C = 22 ft. Cost = 22 2.95 = $64.90 $64.90

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Homework pg. 448 #1-16, 23a, 26 Use formulas

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