Circles
The perimeter of a circle is called the circumference.
The shortest distance from the centre to the circumference is called the radius.
The line across the centre of a circle is the diameter, this is 2 x the radius.
Diameter and radius
Diameter = 2 x radius
D = 2r
Example
Calculate the diameter when the radius is 2.4 cm.
D = 2r
D = 2 x 2.4 = 4.8 cm
Example
Calculate the radius when the diameter is 5 m.
D = 2r
5 = 2 x r
r = 5 ÷ 2 = 2.5 m
Calculating the circumference of a circle
The circumference of a circle is calculated using the formula
Circumference = π x diameter
C = πD
π is the number 3.1415926…
A common approximation is 3.14
There is a π button on most calculators which gives a more accurate value.
Example
Calculate the circumference of this circle.
Circumference = π x diameter
C = πD
C = π ×12
C = 12 π = 37.7 cm (to 1 d.p.)
C = 37.7 cm (to 1 d.p.)
Since π is a decimal number, all answers will need to be rounded.
Example
Calculate the length of ribbon needed to go around a circular birthday cake with a diameter of 22 cm.
The length of the ribbon will be the circumference of the cake.
Circumference = π x diameter
C = πD
C = π ×22
C = 22 π = 69.1 cm (to 1 d.p.)
C = 69.1 cm (to 1 d.p.)
Example
Calculate the length of the circumference with a radius of 8.4 metres.
D = 2r
D = 2 x 8.4 = 16.8 m
Circumference = π x diameter
C = πD
C = 16.8 x π = 52.8 (to 1 d.p.)
C = 52.8 m (to 1 d.p.)
Calculating the area of a circle
The area of a circle is calculated using the formula
Area = π x radius x radius
A = πr²
Example
Calculate the area of this circle.
Area = π x radius x radius
A = πr²
A = π x 8.4²
A = 221.7 m² (to 1 d.p.)
A = 221.7 m² (to 1 d.p.)
Example
Calculate the area of the top of a circular birthday cake with a diameter of 22cm.
D = 22 cm
r = 22 ÷ 2 = 11 cm
A = πr²
A = π x 11² = 380.1 cm²
A = 380.1cm² (to 1 d.p.)
Take care when the diameter is given and the area is required. The radius must be calculated in order to use A = πr²
Question
Calculate the circumference and the area of this circle giving answers to 1 decimal place.
r = 16 mm
D = 32 mm
C = πD
C = π x 32
C = 100.5 mm
A = πr²
A = π x 16²
A = 804.2 mm²
Circumference = 100.5 mm
Area = 804.2 mm²
Test yourself
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