Year 9 Arcs and Sectors Dr J Frost Last modified: 5 th May 2015 Objectives: Be able to calculate the area of a sector,

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Presentation transcript:

Year 9 Arcs and Sectors Dr J Frost Last modified: 5 th May 2015 Objectives: Be able to calculate the area of a sector, the length of an arc, and solve other problems involving area and volume.

12 Area = 18 π Perimeter = π 4 Area = 4 π Perimeter = π ? ? ? ? Area of shaded region = 4 – π 4 ? Starter Give your answers in terms of π.

Edexcel March 2012 What is the perimeter of the shape? ? Typical GCSE example

Exercise 1 Find the perimeter and area of the following shapes in terms of the given variable(s) and in terms of . (Copy the diagram first) 3x 2x ? ? ? ? ? ? ? ? ? ?  1 Area: 3  3 –  Perim: 6   ? ? (Triangle is equilateral)

θ r Arc Sector Area of circle:= π r 2 Circumference of circle: = 2 π r Proportion of circle shaded: = _θ_ 360 Area of sector = π r 2 × _θ_ 360 Length of arc = 2 π r × _θ_ 360 ? ? ? ? ?  Arcs and Sectors ? ?

5 Sector area = Arc length = 4.36 Area = 20 Radius = cm Sector area = 4.04cm 2 Arc length = 3.85cm ? ? ? ? ? 50 ° 105 ° 135 ° (Hint: Plug values into your formula and rearrange) Test Your Understanding 1 2 

Exercise 2 Find the area and perimeter of the following sectors. Give your answers to 3sf. 80  162  125  32  300  87  3cm 6cm 10m2m 3mm 7km Area = 6.28cm 2 Perimeter = 10.2cm Area = 50.9cm 2 Perimeter = 29.0cm Area = 109m 2 Perimeter = 41.8cm Area = 1.12m 2 Perimeter = 5.12m Area = 23.6mm 2 Perimeter = 21.7mm Area = 37.2km 2 Perimeter = 24.6km  120m Chinners Bolt runs round the corner of the semicircular part of the track with radius 120m. He goes 70  around the bend in a time of 15.3s. What was his speed? 9.58m/s 3 The area of the sector is 12cm 2 and its radius 5cm. What is the angle  ? 55.0   5cm 4 Rex and Max want the same amount of dog pizza. Rex takes a slice from a large pizza. Max takes a slice from a small pizza of half the radius. How many times bigger is the angle between the straight sides of Max’s slice? 4 times bigger  ? ? ? ? ? ? ? ? ? ?