Year 9 Arcs and Sectors

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 5th 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 = 18π

Perimeter = 12 + 6π 4

Area = 4π

Perimeter = 8 + 2π

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Area of shaded region = 4 – π

4

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StarterGive your answers in terms of π .

Edexcel March 2012

What is the perimeter of the shape?

𝑃=3𝑥+𝜋 𝑥2?

Typical GCSE example

Exercise 1Find 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

Perimeter: Area:

1

2x

2x

2

Perimeter: Area:

2

5

Perimeter: Area:

3

6

8

Perimeter: Area:

45

2

Perimeter: Area:

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1

Area: 33 – Perim: 63 + 2

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(Triangle is equilateral)

θr

Arc

Sector

Area of circle: = πr2

Circumference of circle:= 2πr

Proportion of circle shaded:

= _θ_360

Area of sector = πr2 × _θ_360 Length of arc = 2πr × _θ_

360

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Arcs and Sectors

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5

Sector area = 10.91

Arc length = 4.36 Area = 20

Radius = 4.122.1cm

Sector area = 4.04cm2

Arc length = 3.85cm

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50°

105°

135°

(Hint: Plug values into your formula and rearrange)

Test Your Understanding

1

2

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Exercise 2Find the area and perimeter of the following sectors. Give your answers to 3sf.

80162

125 32

300 87

3cm6cm

10m 2m

3mm7km

Area = 6.28cm2

Perimeter = 10.2cmArea = 50.9cm2

Perimeter = 29.0cm

Area = 109m2

Perimeter = 41.8cm

Area = 1.12m2

Perimeter = 5.12m

Area = 23.6mm2

Perimeter = 21.7mm

Area = 37.2km2

Perimeter = 24.6km

1 2

70

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 12cm2 and its radius 5cm. What is the angle ?55.0

5cm

4Rex 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

A sector of angle and radius 10cm is used as the net of a cone (with no base). What is its volume?(Note that )

Slant height of cone = 10cm Arc length = Radius of cone Height of cone Volume

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