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

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

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

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

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

7cm Q5 Arcs, Sectors and Segments What is the area and circumference of this cookie (2 d.p.)? 153.94 cm^2 43.98 cm 7cm

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

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

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

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

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

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

6cm Q12 Arcs, Sectors and Segments What is the area of this cookie part (2 d.p.)? (𝜋 x 6^2)/4 cm2 = 28.27 cm^2 6cm

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

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

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

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

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

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

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=82.90313947 〖𝑐𝑚〗^2 SMALL 95/360×𝜋×6^2=29.84513021 〖𝑐𝑚〗^2 B – S = 53.0580… 〖𝑐𝑚〗^2=53.06 〖𝑐𝑚〗^2

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

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

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

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

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

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=26.494 𝑐𝑚

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

Arcs, Sectors and Segments Q26 Arcs, Sectors and Segments What is the perimeter of this shape (2 d.p.)? Arc = 135/360×𝜋×48=56. 54860776𝑐𝑚 Perimeter=Arc+24+24 = 104.55 cm

Arcs, Sectors and Segments Q27 Arcs, Sectors and Segments What is the perimeter of this shape (2 d.p.)? ARC = 270/360×𝜋×44=103.6725576 𝑐𝑚 Length= √(〖22〗^2+〖22〗^2 )=31.11269837 Perimeter = 134.79 cm

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 〗

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 〗

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 〗

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=26.17993878 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×5×5×sin〗⁡〖(120)=10.82531755 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =15.35 〖𝑐𝑚〗^2

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=45.37856055 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×10×10×sin〗⁡〖(52)=39.40053768 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =5.98 〖𝑐𝑚〗^2

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=69.81317008 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×8×8×sin〗⁡〖(125)=26.21286 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =43.60 〖𝑐𝑚〗^2

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=66.66110545 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×13×13×sin〗⁡〖(45.2)=10.82531755 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =15.35 〖𝑐𝑚〗^2

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

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

Arcs, Sectors and Segments EXAM Q’s Arcs, Sectors and Segments Angle = 60 degrees as equilateral 1: SECTOR =60/360×𝜋×6^2=4.71238898 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×6×6×sin〗⁡〖(60)=15.58845727 〖𝑐𝑚〗^2 〗 Area left = Triangle – Sector = 10.9 〖𝑐𝑚〗^2

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

Arcs, Sectors and Segments EXAM Q’s Arcs, Sectors and Segments 1: SECTOR =120/360×𝜋×〖10.4〗^2=113.2648871 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×10.4×10.4×sin〗⁡〖(120)=46.83465384 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =66.4 〖𝑐𝑚〗^2

Arcs, Sectors and Segments EXAM Q’s Arcs, Sectors and Segments 1: SECTOR =40/360×𝜋×8^2=22.34021443 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×8×8×sin〗⁡〖(40)=20.56920351 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =1.77 〖𝑐𝑚〗^2

Arcs, Sectors and Segments EXAM Q’s Arcs, Sectors and Segments 1: SECTOR =35/360×𝜋×〖80〗^2=1954.768762 〖𝑐𝑚〗^2 2: TRIANGLE = 〖1/2×80×80×sin〗⁡〖(35)=1835.444596 〖𝑐𝑚〗^2 〗 Segment = Sector – Triangle =119 〖𝑐𝑚〗^2

Arcs, Sectors and Segments TOUGH Q Arcs, Sectors and Segments Tough Question! ARC = 240/360×𝜋×120=251.3274123 𝑐𝑚 Length= 𝐶𝑜𝑠𝑖𝑛𝑒 𝑟𝑢𝑙𝑒 𝑎^2=𝑏^2+𝑐^2−2𝑏𝑐 cos⁡𝐴 = 94.86832981 cm Perimeter = 346 cm 3 s.f.

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=215.9844949 〖𝑐𝑚〗^2 SMALL110/360×𝜋×〖12〗^2=138.2300768 〖𝑐𝑚〗^2 B – S = 77.75441814 〖𝑐𝑚〗^2 Volume = Cross section x length = 2332.632544〖 𝑐𝑚〗^3= 2330〖 𝑐𝑚〗^3

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=52.35987756 𝑐𝑚 ARC2 = 100/360×𝜋×40=34.90658504 𝑐𝑚 Perimeter = Arc1 + Arc2 + (33x2) = 153.2664626 cm = 153 cm

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.

EXAM Q’s Arcs, Sectors and Segments