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 梅 2 = 2.5 m
Calculating the circumference of a circle
The circumference of a circle is calculated using the formula
Circumference = 蟺 x diameter
C = 蟺D
蟺 is the number 3.1415926鈥
A common approximation is 3.14
There is a 蟺 button on most calculators which gives a more accurate value.
Example
Calculate the circumference of this circle.
Circumference = 蟺 x diameter
C = 蟺D
C = 蟺 脳12
C = 12 蟺 = 37.7 cm (to 1 d.p.)
C = 37.7 cm (to 1 d.p.)
Since 蟺 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 = 蟺 x diameter
C = 蟺D
C = 蟺 脳22
C = 22 蟺 = 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 = 蟺 x diameter
C = 蟺D
C = 16.8 x 蟺 = 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 = 蟺 x radius x radius
A = 蟺r虏
Example
Calculate the area of this circle.
Area = 蟺 x radius x radius
A = 蟺r虏
A = 蟺 x 8.4虏
A = 221.7 m虏 (to 1 d.p.)
A = 221.7 m虏 (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 梅 2 = 11 cm
A = 蟺r虏
A = 蟺 x 112 = 380.1 cm虏
A = 380.1cm虏 (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 = 蟺r虏
Question
Calculate the circumference and the area of this circle giving answers to 1 decimal place.
r = 16 mm
D = 32 mm
C = 蟺D
C = 蟺 x 32
C = 100.5 mm
A = 蟺r虏
A = 蟺 x 16虏
A = 804.2 mm虏
Circumference = 100.5 mm
Area = 804.2 mm虏
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