Transcript 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
271201909145648566923460348610454326648213393607260249141273
724587006606315588174881520920962829254091715364367892590360
011330530548820466521384146951941511609433057270365759591953
092186117381932611793105118548074462379962749567351885752724
891227938183011949129833673362440656643086021394946395224737
190702179860943702770539217176293176752384674818467669405132
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 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:
π≈
22
7
Circle Formulas
Area = πr²
Circumference = 2πr = d π
d
•
r
Exercises
1.
2. C = 12π
5
6
3. A = 16π
4
4. r = 8
8
1. A = π(5)²
A == 25π
____
2. r = ½(12)
r == ____
6
3. r = √16
r == ____
4
4. A = π(8)²
A == 64π
____
C = dπ
C == ____
10π
A = π(6)²
A == ____
36π
C = 2(4)π
C = 8π
____
C = dπ
C = 16π
____
Exercises
5.
C = 100π
50
6. A = 121π
11
5. r = ½(100)
r = ____
50
6. r = √121
r == ____
11
A = π(50)²
A == 2500π
____
C = 2(11)π
C = ____
22π
Exercises
7. Find the diameter of a
pipe if the area of a crosssection is 50.24 cm2
(Use 3.14 for pi)
7. A = πr²
50.24 = 3.14r²
r² = 16
r=4
d=8
___
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 = 3.14d
d=4
r=2
___
Exercises
9. 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
A few together from the HW
• P. 448 # 9 and #12
Homework
pg. 448 #1-16, 23a, 26 Use formulas