Areas of Circles and Sectors

1. Section 10-3
Areas of Circles and Sectors

2. Essential Questions
• How do you find areas of circles?
• How do you find areas of sectors of circles?

3. Vocabulary
1. Sector of a Circle:
2. Segment of a Circle:

4. Vocabulary
1. Sector of a Circle: A region of a circle created by
an angle whose vertex is the center of the
circle (similar to a slice of pie)
2. Segment of a Circle:

5. Vocabulary
1. Sector of a Circle: A region of a circle created by
an angle whose vertex is the center of the
circle (similar to a slice of pie)
2. Segment of a Circle: The region of a circle
bounded by an arc and a chord

6. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.

7. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2

8. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2
r = 72
2
+ 8

9. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2
r = 72
2
+ 8
r = 36 + 8

10. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2
r = 72
2
+ 8
r = 36 + 8
r = 44 in.

11. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2
r = 72
2
+ 8
r = 36 + 8
r = 44 in.
A = π(44)2

12. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2
r = 72
2
+ 8
r = 36 + 8
r = 44 in.
A = π(44)2
A = 1936π

13. Example 1
Fuzzy Jeff Co. manufactures circular covers for outdoor
umbrellas. If the cover is 8 inches longer than the
umbrella on each side, find the area of the cover in
square inches.
A = πr2
r = 72
2
+ 8
r = 36 + 8
r = 44 in.
A = π(44)2
A = 1936π
A ≈ 6082.12 in2

14. Formula for Area of a Sector
A sector of a circle takes up a percentage of the circle. This
percentage is calculated by taking the full circle (360º) and
determining how many degrees the angle formed at the
center takes up. Then, divide that new angle by 360º and
multiply by the area of the circle.

15. Formula for Area of a Sector
A sector of a circle takes up a percentage of the circle. This
percentage is calculated by taking the full circle (360º) and
determining how many degrees the angle formed at the
center takes up. Then, divide that new angle by 360º and
multiply by the area of the circle.
A =
x
360
iπr2

16. Formula for Area of a Sector
A sector of a circle takes up a percentage of the circle. This
percentage is calculated by taking the full circle (360º) and
determining how many degrees the angle formed at the
center takes up. Then, divide that new angle by 360º and
multiply by the area of the circle.
A =
x
360
iπr2
x is the degree of the angle inside the arc

17. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?

18. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?
A =
x
360
iπr2

19. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?
A =
x
360
iπr2 360
10

20. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?
A =
x
360
iπr2 360
10
= 36°

21. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?
A =
x
360
iπr2 360
10
= 36°
A =
36
360
iπ(4)2

22. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?
A =
x
360
iπr2 360
10
= 36°
A = 1.6π
A =
36
360
iπ(4)2

23. Example 2
A pumpkin pie is cut into 10 congruent pieces. If the radius
of the pie is 4 inches, what is the area that one slice of the
pie takes up in the pie tin?
A =
x
360
iπr2 360
10
= 36°
A = 1.6π
A ≈ 5.03 in2
A =
36
360
iπ(4)2

24. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.

25. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2

26. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2
A =
152
360
iπ(7.4)2

27. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2
A =
152
360
iπ(7.4)2
A ≈ 72.64 cm2

28. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.

29. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2

30. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2
A =
360 − 75
360
iπ(4.2)2

31. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2
A =
360 − 75
360
iπ(4.2)2
A =
285
360
iπ(4.2)2

32. Example 3
Find the area of the shaded sector. Round to the nearest
hundredth.
A =
x
360
iπr2
A =
360 − 75
360
iπ(4.2)2
A ≈ 43.87 in2
A =
285
360
iπ(4.2)2

33. Problem Set

34. Problem Set
p. 745 #3-7 all, 9-25 odd
“Nothing is impossible, the word itself says 'I'm
possible’!” - Audrey Hepburn