**Key Terms**

- Arc Length – The length of an arc of a circle.
- Radian – A unit of angular measure determined by the condition: The central angle of one radian in a circle of radius 1 produces an arc of length 1.

**Review**

- Diameter
- The diameter of a circle equals 2 radii
- d = 2 r

- Pi
- Symbol: π
- π’s approximation:

**Notes**

- Circumference
- Describes the distance around a circle
- Measured in units (units, feet, inches, cm, m, etc.)
- As the radius gets bigger, the circumference gets bigger.
- The circumference is about 3 times the radius.

- Circumference Formula
- C = 2 π r
- 2 times Pi times the radius

- C = π d
- Pi times the diameter
- Remember: a diameter equals 2 radii

- C = 2 π r

- Arcs
- Part of a circle
- Can be measured in degrees and in units (length)

- Formula to Find the Measure of an Arc length (in units)
- Divide the arc’s degree measure by 360, then multiply by the circumference of the circle.
- See examples 6 – 8 (below)

- Radians
- The radian is a constant of proportionality.
- For any circle, the central angle measure (in radians) describes the ratio (fraction) between the radius and the arc length
- There are π (pi) radians in a half-circle
- There are 2 π (pi) radians in a full circle
- This is why the circumference is measured with 2 π r

**Examples**

- Ex 1. What is the approximate circumference of the circle shown below?
- Setup: C = 2 π r
- Substitute: 2(3.14)(9)
- Answer: 56.52 cm

- Ex 2. What is the approximate circumference of the circle shown below?
- Setup: π d, so (3.14)(15.5)
- Answer: 48.7 cm

- Ex 3. If you know the circumference of a circle, which step(s) can you follow to find its diameter?
- Setup: C = π d, so you need to isolate the d.
- Answer: Divide by π on both sides to isolate the d
- It would look like:

- Setup: C = π d, so you need to isolate the d.

- Ex 4. The radius of a circular park is 107 m. To the nearest meter, what is the circumference of the park?
- Setup: C = 2 π r
- Substitute: C = 2(3.14)(107)
- Answer: 672 m

- Ex 5. A blu-ray disk is shaped like a circle with a diameter of 12 cm. To the nearest centimeter, what is the circumference of the disk?
- Setup: C = π d
- Substitute: C = (3.14)(12)
- Answer: 38cm

- Ex 6. The circumference of is 72 cm. What is the length of (the minor arc)?
- Setup:
- Simplify:
- Answer: 18 cm

- Ex 7. The length of (the minor arc) is 22 cm. What is the circumference of ?
- Setup:
- Simplify:
- Multiply both sides by 24:
- Answer: 528 cm

- Ex 8. In the diagram below, what is the approximate length of the minor arc ?
- What’s missing? You need to find the circumference! Use C = 2 π r
- C = 2(3.14)(33)
- So, C = 207.345 cm
- Setup:
- Simplify:
- Answer: 34.6 cm