Transcript Slide 1

GCSE: Circles
Dr J Frost ([email protected])
Last modified: 6th October 2013
Starter
Give your answers in terms of π
4
Area of shaded
region = 4 –? π
12
Area
= 4π
?
Perimeter = 8 +?2π
4
Area
= 18π
?
Perimeter = 12 +? 6π
Typical GCSE example
Edexcel March 2012
What is the perimeter of the shape?
P = 3x +? pi x / 2
Exercises
Find the perimeter and area of the following shapes in terms of the given variable(s)
and in terms of . (Copy the diagram first)
3
2
1
2x
2x
5
3x
2x
Perimeter: 8𝑥 + 𝜋𝑥
?1
Area:
6𝑥 2 +?2 𝜋𝑥 2
4
Perimeter: 6𝑥 + 𝜋𝑥
?1
Area:
4𝑥 2 −?2 𝜋𝑥 2
5
2
Perimeter: 2 + 3𝜋
?
𝜋
Area:
4 − 2?
8
6
Perimeter: 14 + 5𝜋
?
25
Area:
24 + ? 𝜋
2
2
Perimeter: 10 + 𝜋?
Area:
6 + 𝜋?
Arcs and Sectors
Arc
Area of circle:
Circumference of circle:
= 2πr?
θ
r
(Write down)
Area of sector =
= πr2?
πr2
Proportion of circle
shaded:
_θ_
= ?
360
Sector
_θ_
×?
360
_θ_
Length of arc = 2πr ×?
360
Practice Questions
Sector area = 10.91
?
Area = 20
50°
5
Arc length = 4.36
?
Sector area = 4.04cm
? 2
105°
2.1cm
?
Arc length = 3.85cm
135°
(Hint: Plug values into your
formula and rearrange)
Radius = 4.12
?
A* GCSE questions
?
Area of triangle = 3√27
Area of sector = 1.5π
?
Area of shaded region = 3√27 - 1.5π
? = 10.9cm2
Helpful formula:
Area of triangle = ½ ab sin C
Difficult A* Style Question
The shape PQR is a minor sector.
The area of a sector is 100cm2.
The length of the arc QR is 20cm.
Q
a) Determine the length PQ.
P
?
Answer: 10cm
R
b) Determine the angle QPR
Answer: 114.6°
?
Bonus super hard question:
Can you produce an inequality
that relates the area A of a sector
to its arc length L?
L < ?4πA
Hint: Find an expression
for θ. What constraint is
on this variable?
Exercises
Rayner GCSE Pg 191
Exercise 17C: Q2, 3, 10, 11, 12
Exercise 18C: Q9, 10, 13, 17, 19, 22