1. Learning Target #20 Arc Length and Sector Areas
Circumference
Sectors

2. REVIEW: RADIUS AND DIAMETER
The RADIUS is the measure of any radius.
Radius is usually abbreviated as .
The DIAMETER is the measure of any diameter.
Diameter is usually abbreviated as . r d

3. CIRCUMFERENCE: or If you unwrap a circle, how long will the line be?
The distance around the circle.
If you unwrap a circle, how long will the line be? or
So what is  anyway?

4. Example: Find the Circumference of the Circle
Exact Answer cm cm
Approximate Answer

5. For area the units are always squared!
The area of a region is the number of unit squares that can fit into the region (or the space inside the region.)
The area of a unit square
= length X width
= (1 cm) X (1 cm)
= 1X1 X cm x cm
= 1 cm2
For area the units are always squared!
Unit
Square

6. AREA
The area of a circle is the number of unit squares that can fit into the circle.
How many squares are in the circle?
You can estimate by counting…
Or use the formula!

7. AREA FORMULA r The area of a circle with radius r is given by
This gives us the EXACT number of squares! r
(It’s usually not a whole number.)

8. Example: Find the Area of the Circle
Exact Answer
Find the area of the following circle.
cm2
cm2
Approximate Answer

9. Fraction of a Circle
What fraction of the whole circle is a given arc?
Find the measure of the central angle.
Divide by 360, the total number of degrees in the circle.
180º
diameter
This arc is one-half of a circle.

10. Fraction of a Circle What fraction of the whole circle is this arc?
Find the measure of the central angle.
Divide by 360, the total number of degrees in the circle.
This arc is one-fifth of a circle.

11. Fraction of a Circle 140º 220º = 220º
What fraction of the whole circle is this (major) arc?
Find the measure of the central angle.
The major arc measure is:
360º – minor arc measure
= 360º - 140º
= 220º
Divide by 360, the total number of degrees in the circle.
140º
220º
This arc is eleven-eighteenths of a circle.

12. Fraction of a Circle
What fraction of the whole circle is a given arc?
Find the measure of the central angle.
Divide by 360, the total number of degrees in the circle. a
Fraction of the circle =

13. Arc Length The distance around an arc
The amount of crust on a slice of pizza.
The ratio of the center angle and 360° (the FRACTION OF THE CIRCLE) multiplied by the CIRCUMFERENCE

14. Arc Length Formula Arc Length
= (fraction of the circle) X (circumference)
= fr x C
= x 2r
= x 2r

15. Example: Find the Arc Length
A.L. (arc length)
= fraction *circ. =
Exact Answer (in terms of ) in in
Approximate Answer (nearest tenth)

16. SECTOR
sector of a circle - part of the interior of a circle bounded by two radii and an arc.

17. AREA OF A SECTOR
The area of a sector of a circle
The size of a slice of pizza.
The FRACTION OF THE CIRCLE multiplied by the AREA OF THE CIRCLE.

18. Area of a Sector Formula
= (fraction of the circle) X (area of circle)
= fr x A
= X r2

19. Example: Find the Area of the Sector
A.S. (area of a sector)
= fraction *area
72°
Exact Answer (in terms of )
in2
Approximate Answer (nearest tenth)
in2