Geometry 11 5 Circumference and Area of Circles

Geometry 11. 5 Circumference and Area of Circles

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

The Value of Pi……… PI 3. 141592653589793238462643383279502884197169399375105820974944 592307816406286208998628034825342117067982148086513282306647 093844609550582231725359408128481117450284102701938521105559 644622948954930381964428810975665933446128475648233786783165 ER B M 271201909145648566923460348610454326648213393607260249141273 U N L 724587006606315588174881520920962829254091715364367892590360 A N 011330530548820466521384146951941511609433057270365759591953 O I AT 092186117381932611793105118548074462379962749567351885752724 R IR 891227938183011949129833673362440656643086021394946395224737 n a 190702179860943702770539217176293176752384674818467669405132 is i P 000568127145263560827785771342757789609173637178721468440901 224953430146549585371050792279689258923542019956112129021960 864034418159813629774771309960518707211349999998372978049951 …and so on, never terminating, never repeating…….

Approximate Value of Pi……… 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 6 aπ, 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: π≈ 22 7

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

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

Exercises Find the diameter of a pipe if the area of a cross-section is 50. 24 cm 2 (Use 3. 14 for pi 7. A = πr² 50. 24 = 3. 14 r² r² = 16 r=4 d=8 Find the radius of a pizza pan if its circumference is 12. 56 ft. (Use 3. 14 for pi) 8. C = dπ 12. 56 = 3. 14 d d=4 r=2

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) 9 $64. 0 C = 7(22/7) C = 22 ft. Cost = 22 • 2. 95 = $64. 90

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