GCSE: Circles
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GCSE: Circles. Dr J Frost ([email protected]) . Last modified: 6 th October 2013. Starter. Give your answers in terms of π. 4. Area of shaded region = 4 – π. ?. 12. Area = 4 π. ?. Perimeter = 8 + 2 π. ?. Area = 18 π. ?. Perimeter = 12 + 6 π. - PowerPoint PPT Presentation
Transcript of GCSE: Circles
12
Area = 18π
Perimeter = 12 + 6π 4
Area = 4π
Perimeter = 8 + 2π
Give your answers in terms of π
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Area of shaded region = 4 – π
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Starter
Edexcel March 2012
What is the perimeter of the shape?
P = 3x + pi x / 2?
Typical GCSE example
ExercisesFind 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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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
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)
Practice Questions
A* GCSE questions
Area of triangle = 3√27
Area of sector = 1.5π
Area of shaded region = 3√27 - 1.5π = 10.9cm2
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Helpful formula:Area of triangle = ½ ab sin C
The shape PQR is a minor sector.The area of a sector is 100cm2.The length of the arc QR is 20cm.
a) Determine the length PQ.
Answer: 10cm
b) Determine the angle QPR
Answer: 114.6°
P
Q
R
Bonus super hard question:Can you produce an inequality that relates the area A of a sector to its arc length L?
L < 4πAHint: Find an expression for θ. What constraint is on this variable?
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Difficult A* Style Question
Exercises
Rayner GCSE Pg 191Exercise 17C: Q2, 3, 10, 11, 12Exercise 18C: Q9, 10, 13, 17, 19, 22
