1. CIRCLES

2. HINT: Pi =3.14

3. Geometry Lessons 8.5 and 8.6 Area of Circles, Sectors and Segments
HW: 8.5/1-8, 12-14
8.6/1-12

4. Circumference
3in
C ≈ 18.8in

5. Finding a formulae for the area of a circle

6. πr r

7. Area of Rectangle= Base x Height

8. Finding the area given the diameter
The radius of a circle is half of its diameter, or
r = d 2
We can substitute this into the formula
A = πr2

9. How to find the area of a circle given the radius
Find the area of the circle below:
Substitute the values for p and r.

10. How to find the area of a circle
given the diameter
Given the diameter:
Radius = diameter divided by 2
Substitute the values for p and r.

11. How would you find the shaded area?
Find the area of the square and subtract the area of the circle.

12. The area of a circle
Use π = 3.14 to find the area of the following circles:
2 cm
10 m
A = πr2
A = πr2
= 3.14 × 22
= 3.14 × 52
Explain that rather than use the formula on the previous slide, it is usually easier to halve the diameter mentally to give the radius, before substituting it into the formula.
The most common error is to neglect to half the diameter to find the radius and to substitute this value into the formula. Ensure that pupils do not make this mistake.
= cm2
= 78.5 m2
23 mm
78 cm
A = πr2
A = πr2
= 3.14 × 232
= 3.14 × 392
= mm2
= cm2

13. Find the area of this shape
Use π = 3.14 to find area of this shape.
The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm.
Compare this with slide 74, which finds the perimeter of the same shape.
Area of circle = 3.14 × 6.52
13 cm
6 cm
= cm2
Area of rectangle = 6 × 13
= 78 cm2
Total area =
= cm2

14. The circumference of a circle is 18
The circumference of a circle is 18. Find the area of the circle, leave answer in terms of .
C = 2  r
A = r2
A = 92
A = 81
18 = 2r
9 = r

15. Arc Length Reminder The length of part of the circumference.
The length of the arc depends on what two things?
1) The measure of the arc.
2) The size of the circle.
An arc length measures distance while
the measure of an arc is in degrees.

16. m 2πr 360 . Arc Length Formula measure of the central angle or arc
The circumference of the
entire circle!
2πr
Arc Length =
360
The fraction of the circle! .

17. REVIEW: Finding Arc Length
Find the arc length. Give answers in terms of  and rounded to the nearest hundredth. FG
Use formula for area of sector.
Substitute 8 for r and 134 for m.
Simplify.
 5.96 cm  cm

18. Sectors
Let’s talk pizza

19. Sector of a circle
A region bounded by 2 radii and their intercepted arc. .

20. Area of a Sector Formula
measure of the central angle or arc m˚
πr2
Area of a sector =
360
The area of the entire circle!
The fraction of the circle! .

21. Finding the Area of a Sector
Find the area of the sector. Give answers in terms of  and rounded to the nearest hundredth.
sector HGJ
Use formula for area of sector.
Substitute 12 for r and 131 for m.
Simplify.
= 52.4 m2  m2

22. Finding the Area of a Sector
Find the area of the sector. Give answers in terms of  and rounded to the nearest hundredth.
sector ABC
Use formula for area of sector.
Substitute 5 for r and 25 for m.
Simplify.
 1.74 ft2  5.45 ft2

23. The area of sector AOB is
and
Find the radius of ○O. m
Area of a sector =
πr2
360 9 40
π =
πr2 4
360 9 9 1 9 = r2 1 4 9 1 81 = r2 4 9
r = 2

24. The area of sector AOB is 48π and
Find the radius of ○O. m
πr2
Area of a sector =
360
270
48π =
πr2
360 A O 4 16 3 4 r2
48 = 3 4 3
64 = r2 r
= 8 B

25. Finding the Area of a Sector
Find the area of each sector. Give your answer in terms of  and rounded to the nearest hundredth.
sector JKL
Use formula for area of sector.
Substitute 16 for r and 36 for m.
Simplify.
= 25.6 in2  in2

26. Automobile Application
A windshield wiper blade is 18 inches long. To the nearest square inch, what is the area covered by the blade as it rotates through an angle of 122°?
Use formula for area of sector.
r = 18 in. m˚ = 122˚
Simplify.
 345 in2

27. AREA OF SEGMENT
A segment of a circle is a region bounded by an arc and its chord.

29. = ¼100π= 25π 10
=½∙10∙10=50
Area of Segment = 25π - 50

30. Check It Out!
Find the area of segment RST to the nearest hundredth.
Step 1 Find the area of sector RST.
Use formula for area of sector.
Substitute 4 for r and 90 for m.
= 4 m2
Simplify.

31. Check It Out! Continued
Find the area of segment RST to the nearest hundredth.
Step 2 Find the area of ∆RST.
ST = 4 m, and RS = 4m.
Simplify.
= 8 m2

32. Check It Out! Continued
Find the area of segment RST to the nearest hundredth.
Step 3
area of segment = area of sector RST – area of ∆RST
= 4 – 8
 4.57 m2

33. Lesson Quiz: Part I
Find each measure. Give answers in terms of  and rounded to the nearest hundredth.
1. area of sector LQM
7.5 in2  in2
2. length of NP
2.5  in.  7.85 in.

34. Lesson Quiz: Part II
3. The gear of a grandfather clock has a radius of 3 in. To the nearest tenth of an inch, what distance does the gear cover when it rotates through an angle of 88°?
 4.6 in.
4. Find the area of segment GHJ to the nearest hundredth.
 m2

35. Find the area of the shaded region
Find the area of the shaded region. Point O marks the center of the circle. 8. 9.
10.
11.
60˚ 8 12
60 O 6 4
30 O O
160
π units2
9π - 18 units2
24π - 36√3 units2
8π - 8√3 units2 3

36. Some common fractions and measures!
Arc or Central Angle Measure
Fraction of the Circle
36o
108o
1/6
5/6
120o
2/3
30o
11/12
1/8
5/8
3/10
1/10
60o
300o
1/3
240o
1/12
330o
45o
225o