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. The symbol for pi is π This ratio is the same for all circles. d π = C d

PI …and so on, never terminating, never repeating……. Pi is an IRRATIONAL NUMBER The Value of Pi………

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

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

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

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

Exercises 7. A = πr² Find the diameter of a pipe if the area of a cross-section is cm 2 (Use 3.14 for pi Find the radius of a pizza pan if its circumference is ft. (Use 3.14 for pi) = 3.14r² r² = 16 r = 4 d = 8 8. C = dπ = 3.14d 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) C = 7(22/7) C = 22 ft. Cost = = $64.90 $64.90

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