Circumference and area of circles
Definitions
Diameter D is the width of the circle, from one side
D
to another.
Radius is half the diameter = distance from centre to edge.
r
We can calculate diameter = 2× radius,
D  2r
We can calculate radius = half the diameter, r 
D
2
Circumference is the distance around the outside of the circle (for any other shape we
would call this the perimeter).
Circumference   D
or
Circumference  2 r
(same thing!)
 (“Pi”) is defined as the circumference ÷ diameter.
You don’t need to know how its value is calculated!
 = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944
5923078164 0628620899 8628034825 3421170679 ...it goes on for ever. We use the
 button on the calculator to save having to type it in.
Area is the amount of surface inside the circle, measured in units such as square
metres (m2).
Area   r 2
D
Examples
A gas holder is 60 m diameter. I want to walk around it. How far is it around?
D = 60 m.
Circumference =  D    60  199.5 m (to 1 decimal place).
If I want to hold a party on top of it, and each person needs 1 m2 space to stand in, how
many people can I invite?
Area =  r    30  2827 m so I can invite 2826 friends.
2
2
2
Perimeter and area of sectors.

A sector may be half a circle, a quarter of a circle etc.
For perimeter:
 Find the diameter D
 Write a formula for a fraction of
the circumference  D + 1
diameter for the straight edges.
 Put numbers in the formula
For area:
 Find the radius
 Write a formula for a fraction of
the circle area  r
Put numbers in the formula.
2

Half a circle:
5m
D=5m
Perimeter =
D
2
D
 5
2
 5  12.85 m
r = 2.5 m
Area of half a circle =
 r2
2

  2.52
2
 19.6 m2