0. 14cm Bellwork Arcs, Sectors and Segments It’s Big Cookie Thursday!!!
The diameter of Mr Horrocks cookie is 14 cm
What is the radius of the cookie?
What is the area of the cookie to 3.s.f ?
What is the circumference of the cookie to 3.s.f.?
14cm
7cm
𝜋 x 72=145cm^2
𝜋 x 14 = 44.0cm

1. 8cm Q1 Arcs, Sectors and Segments
What is the area of this cookie (3.s.f.)?
8cm
50.3 cm^2

2. 4cm Q2 Arcs, Sectors and Segments
What is the area of this cookie (2 d.p.)?
50.27 cm^2
4cm

3. 8cm Q3 Arcs, Sectors and Segments
What is the circumference of this cookie (3.s.f.)?
8cm
25.1cm

4. 16cm Q4 Arcs, Sectors and Segments
What is the circumference of this cookie (1 d.p.)?
100.5 cm
16cm

5. 7cm Q5 Arcs, Sectors and Segments
What is the area and circumference of this cookie (2 d.p.)?
cm^2
43.98 cm
7cm

6. 10cm Q6 Arcs, Sectors and Segments
What is the area and circumference of this cookie (3.s.f.)?
10cm
78.5 cm^2
31.4 cm

7. 3cm Q7 Arcs, Sectors and Segments
What is the area of this cookie (leave your answer in terms of π)?
9𝜋 cm2
3cm

8. 8cm Q8 Arcs, Sectors and Segments
What is the circumfernce of this cookie (leave your answer in terms of π)?
16𝜋 cm
8cm

9. 4cm Q9 Arcs, Sectors and Segments
What is the circumfernce of this cookie (leave your answer in terms of π)?
4cm
4𝜋 cm

10. 10cm Q10 Arcs, Sectors and Segments
What is the area of this cookie (leave your answer in terms of π)?
10cm
25𝜋 cm2

11. 14cm Q11 Arcs, Sectors and Segments
Mr Sargeson is generous, giving half his cookie to Mr Macphail.
What area of cookie do they get each (3 s.f)?
(𝜋 x 7^2)/2 cm2
= 77.0 cm^2
14cm

12. 6cm Q12 Arcs, Sectors and Segments
What is the area of this cookie part (2 d.p.)?
(𝜋 x 6^2)/4 cm2
= cm^2
6cm

13. Arcs, Sectors and Segments
Q13
Arcs, Sectors and Segments
What is the area of this sector (3 s.f.)?
150/360×𝜋×〖13〗^2=221 〖𝑐𝑚〗^2

14. Arcs, Sectors and Segments
Q14
Arcs, Sectors and Segments
What is the area of this sector (1 d.p.)?
45/360×𝜋×〖11〗^2=47.5 〖𝑐𝑚〗^2

15. Arcs, Sectors and Segments
Q15
Arcs, Sectors and Segments
What is the area of this sector (1 d.p.)?
200/360×𝜋×6^2=62.8 〖𝑐𝑚〗^2

16. Arcs, Sectors and Segments
Q16
Arcs, Sectors and Segments
What is the area of this sector (3 s.f.)?
85/360×𝜋×〖25〗^2=464 〖𝑚𝑚〗^2

17. Arcs, Sectors and Segments
Bellwork
Arcs, Sectors and Segments
What is the area of this sector (3 s.f.)?
150/360×𝜋×〖55〗^2=3960 〖𝑚𝑚〗^2

18. Arcs, Sectors and Segments
Q17
Arcs, Sectors and Segments
What is the area of this sector (3 s.f.)?
300/360×𝜋×〖15〗^2=589 〖𝑐𝑚〗^2

19. Arcs, Sectors and Segments
Q18
Arcs, Sectors and Segments
What is the area of the shaded area (2 d.p.)?
6 cm
10 cm
BIG 95/360×𝜋×〖10〗^2= 〖𝑐𝑚〗^2
SMALL 95/360×𝜋×6^2= 〖𝑐𝑚〗^2
B – S = … 〖𝑐𝑚〗^2=53.06 〖𝑐𝑚〗^2

20. Arcs, Sectors and Segments
Q19
Arcs, Sectors and Segments
What is the length of this arc (2 d.p.)?
60/360×𝜋×8=4.19 𝑐𝑚

21. Arcs, Sectors and Segments
Q20
Arcs, Sectors and Segments
What is the length of this arc AB (3 s.f.)?
80/360×𝜋×12=16.8 𝑐𝑚

22. Arcs, Sectors and Segments
Q21
Arcs, Sectors and Segments
What is the length of this arc AB (2 d.p.)?
120/360×𝜋×60=62.83 𝑐𝑚

23. Arcs, Sectors and Segments
Q22
Arcs, Sectors and Segments
What is the length of this arc AB (3 s.f.)?
210/360×𝜋×120=220 𝑐𝑚

24. Arcs, Sectors and Segments
Q23
Arcs, Sectors and Segments
What is the length of this arc AB (1 d.p.)?
60/360×𝜋×14.6=7.6 𝑐𝑚

25. Arcs, Sectors and Segments
Q24
Arcs, Sectors and Segments
What is the length of this arc AB (3 d.p.)?
330/360×𝜋×9.2= 𝑐𝑚

26. Arcs, Sectors and Segments
Q25
Arcs, Sectors and Segments
What is the length of this arc AB (3 s.f.)?
270/360×𝜋×160=377 𝑚𝑚

27. Arcs, Sectors and Segments
Q26
Arcs, Sectors and Segments
What is the perimeter of this shape (2 d.p.)?
Arc = 135/360×𝜋×48= 𝑐𝑚
Perimeter=Arc = cm

28. Arcs, Sectors and Segments
Q27
Arcs, Sectors and Segments
What is the perimeter of this shape (2 d.p.)?
ARC = 270/360×𝜋×44= 𝑐𝑚
Length= √(〖22〗^2+〖22〗^2 )=
Perimeter = cm

29. Arcs, Sectors and Segments
Calculate the Area of this triangle (1 d.p.)
〖1/2 absin〗⁡𝐶
〖1/2×8.4×7.1×sin〗⁡〖(49)=22.5 〖𝑐𝑚〗^2 〗

30. Arcs, Sectors and Segments
Q35
Arcs, Sectors and Segments
Calculate the Area of this triangle (1 d.p.)
〖1/2 absin〗⁡𝐶
〖1/2×15.6×17.8×sin〗⁡〖(28)=65.2 〖𝑐𝑚〗^2 〗

31. Arcs, Sectors and Segments
Q36
Arcs, Sectors and Segments
Calculate the Area of this triangle (1 d.p.)
30o
8 cm
〖1/2 absin〗⁡𝐶
〖1/2×8×8×sin〗⁡〖(30)=16 〖𝑐𝑚〗^2 〗

32. Arcs, Sectors and Segments
Q37
Arcs, Sectors and Segments
Work out the area of the Segment (2 d.p.)
HINT
1: SECTOR =120/360×𝜋×5^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×5×5×sin〗⁡〖(120)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =15.35 〖𝑐𝑚〗^2

33. Arcs, Sectors and Segments
Q38
Arcs, Sectors and Segments
Work out the area of the Segment (2 d.p.)
1: SECTOR =52/360×𝜋×〖10〗^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×10×10×sin〗⁡〖(52)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =5.98 〖𝑐𝑚〗^2

34. Arcs, Sectors and Segments
Q39
Arcs, Sectors and Segments
Work out the area of the Segment (2 d.p.)
1: SECTOR =125/360×𝜋×8^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×8×8×sin〗⁡〖(125)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =43.60 〖𝑐𝑚〗^2

35. Arcs, Sectors and Segments
Q40
Arcs, Sectors and Segments
Work out the area of the Segment (2 d.p.)
ANGLE CosA=(〖13〗^2+〖13〗^2−〖10〗^2)/(2×13×13) A=45.2
1: SECTOR =45.2/360×𝜋×〖13〗^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×13×13×sin〗⁡〖(45.2)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =15.35 〖𝑐𝑚〗^2

36. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
Arc=60/360×𝜋×24=4𝜋 𝑐𝑚

37. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
Arc=120/360×𝜋×12=4𝜋 𝑐𝑚
Perimeter = 4𝜋+12 𝑐𝑚

38. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
Angle = 60 degrees as equilateral
1: SECTOR =60/360×𝜋×6^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×6×6×sin〗⁡〖(60)= 〖𝑐𝑚〗^2 〗
Area left = Triangle – Sector = 10.9 〖𝑐𝑚〗^2

39. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
Arc = 120/360×𝜋×20.8=21.8 𝑐𝑚

40. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
1: SECTOR =120/360×𝜋×〖10.4〗^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×10.4×10.4×sin〗⁡〖(120)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =66.4 〖𝑐𝑚〗^2

41. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
1: SECTOR =40/360×𝜋×8^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×8×8×sin〗⁡〖(40)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =1.77 〖𝑐𝑚〗^2

42. Arcs, Sectors and Segments
EXAM Q’s
Arcs, Sectors and Segments
1: SECTOR =35/360×𝜋×〖80〗^2= 〖𝑐𝑚〗^2
2: TRIANGLE = 〖1/2×80×80×sin〗⁡〖(35)= 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =119 〖𝑐𝑚〗^2

43. Arcs, Sectors and Segments
TOUGH Q
Arcs, Sectors and Segments
Tough Question!
ARC = 240/360×𝜋×120= 𝑐𝑚
Length= 𝐶𝑜𝑠𝑖𝑛𝑒 𝑟𝑢𝑙𝑒 𝑎^2=𝑏^2+𝑐^2−2𝑏𝑐 cos⁡𝐴 = cm
Perimeter = 346 cm
3 s.f.

44. Arcs, Sectors and Segments
TOUGH Q
Arcs, Sectors and Segments
The diagram shows a prism whose cross-section is the area between two sectors.
OA = 12 centimetres
OC = 15 centimetres.
Calculate the volume of this prism.
3 s.f.
BIG 110/360×𝜋×〖15〗^2= 〖𝑐𝑚〗^2
SMALL110/360×𝜋×〖12〗^2= 〖𝑐𝑚〗^2
B – S = 〖𝑐𝑚〗^2
Volume = Cross section x length = 〖 𝑐𝑚〗^3= 2330〖 𝑐𝑚〗^3

45. Arcs, Sectors and Segments
TOUGH Q
Arcs, Sectors and Segments
In the diagram PQ and RS are arcs of circles with centre O.
The radius, OQ, is 30 centimetres long and the radius,
OS, is 20 centimetres long.
Calculate the perimeter of this shape
3 s.f.
ARC1 = 100/360×𝜋×60= 𝑐𝑚
ARC2 = 100/360×𝜋×40= 𝑐𝑚
Perimeter = Arc1 + Arc2 + (33x2) = cm = 153 cm

46. TOUGH Q
Arcs, Sectors and Segments
The diagram below shows an ornamental garden.
The garden is in the shape of a rectangle with a sector of a circle added at one end.
The length of the garden is 35 metres and its breadth is 20 metres.
(a) Calculate OB the radius of the sector.
(b) Find the perimeter of the garden.

47. EXAM Q’s
Arcs, Sectors and Segments