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© www.teachitmaths.co.uk 2012 16806
The circumference of a circle
1 © www.teachitmaths.co.uk 2012 16806
1 1½ 2 2½
4
The circumference of a circle
Diameter
Approximately how many diameters fit all the way round the
circumference?
Choose your answer:
3½ 3
2
© www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Diameter
1
2
3
Approximately 31/7 diameters fit around the circumference.
The actual figure is:3.14159265358...
This number is called π (pi).
Circumference = π × diameterC = πd
Or using the radius;C = 2πr
3
1/7
© www.teachitmaths.co.uk 2012 16806
The circumference of a circle
This rule is the same for all circles!
4
© www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Examples: Find the circumference of these circles.
C = πd
C = 2πr
8cm 9.5cm
C = πd
C = π × 8
C = 25.1cm (1 d.p.)
C = πd
C = π × 9.5
C = 29.8cm (1 d.p.)
5 © www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Examples: Find the circumference of these circles.
C = πd
C = 2πr
C = 2πr
C = 2 × π × 2.1
C = 13.2m (1 d.p.)
C = 2πr
C = 2 × π × 3
C = 18.8mm (1 d.p.)
6
2
© www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Examples: Find the circumference of the tyre and the steering wheel.
C = πd
C = 2πr
C = πd
C = π × 23
C = 72.3cm (1 d.p.)
C = 2πr
C = 2 × π × 7.5
C = 47.1cm (1 d.p.)
23cm
7.5cm
7 © www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Examples: Find the perimeters of these shapes.
C = πd
C = 2πr
8cm
9.5cm
Perimeter = ½ × Circumference + diameter
P = ½πd + d
P = ½π × 8 + 8
C = 20.6cm (1 d.p.)
P = ½πd + d
P = ½π × 9.5 + 9.5
C = 24.4cm (1 d.p.)
8
© www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Examples: Find the perimeters of these shapes.
C = πd
C = 2πr
6cm8.5cm
P = ¼ × 2πr + 2r
P = ¼ × 2π × 6 + 2 × 6
C = 21.4cm (1 d.p.)
P = ¾ × 2πr + 2r
P = ¾ × 2π × 8.5 + 2 × 8.5
C = 57.1cm (1 d.p.)
9 © www.teachitmaths.co.uk 2012 16806
The circumference of a circle
Examples:
C = πd
C = 2πr
C = πd
d = C/π
d = 25/π
d = 8.0cm (1 d.p.)
C = 2πr
r = C/2π
r = 30/2π
r = 4.8cm (1 d.p.)
C = 30cm. Find the radius.
10
C = 25cm. Find the diameter.