3.2.3 Circumference
Circumference is the distance around a circle. It is the perimeter of a circle. The circumference of a circle is given by the formula:
C = πD or C = 2πr
Where:
- C is the circumference
- π = 22/7 or 3.142
- D is the diameter
- r is the radius
Perimeter of an Arc
C = (θ / 360) × πD
Where C is the length of the curved surface, θ is the angle between the radii of the sector and D is the diameter.
Summary Table
Example 3.7
Calculate the circumference of a circle of radius 3.5 cm.
Solution:
C = 2πr
C = 2 × 22/7 × 3.5
C = 22 cm
Example 3.8
The figure below shows a running track. Kiptoo runs 5 rounds in the track. What distance does he run?
Solution:
The distance can be divided into two semi-circles and two straight distances.
P = ½ × 22/7 × 70 + 100 + 100 + ½ × 22/7 × 70
P = 110 + 100 + 100 + 110
P = 420 m
Distance for 5 rounds = 5 × 420 = 2100 metres
Example 3.9
The figure below shows a plot of land in the shape of a quarter circle. Calculate the perimeter of the plot.
Solution:
P = ¼πD + 2r
P = ¼ × 2 × 22/7 × 140 + 2 × 140
P = 220 + 280
P = 500 metres
Circle Mathematics Practice
1. The radius of a circle is 7 cm. The circle is divided into two equal parts. What is the perimeter of each circular part?
Perimeter of each part = 36 cm
Radius = 7 cm
Circumference = 2πr = 2 × 22/7 × 7 = 44 cm
Half circumference = 44 ÷ 2 = 22 cm
Diameter = 14 cm
Perimeter = 22 + 14 = 36 cm
Circumference = 2πr = 2 × 22/7 × 7 = 44 cm
Half circumference = 44 ÷ 2 = 22 cm
Diameter = 14 cm
Perimeter = 22 + 14 = 36 cm
2. If the circumference of a circular sheet is 154 m, find its diameter.
Diameter = 49 m
Circumference = πd
154 = 22/7 × d
d = 154 × 7 ÷ 22 = 49 m
154 = 22/7 × d
d = 154 × 7 ÷ 22 = 49 m
3. The diameter of a car wheel is 70 cm. Find the distance covered in 10 revolutions in metres.
Distance covered = 22 metres
Circumference = πd = 22/7 × 70 = 220 cm
Distance for 10 revolutions = 220 × 10 = 2200 cm
Convert to metres: 2200 ÷ 100 = 22 m
Distance for 10 revolutions = 220 × 10 = 2200 cm
Convert to metres: 2200 ÷ 100 = 22 m
4. Find the perimeter of the figure below.
Perimeter = Depends on given measurements
Add the lengths of all straight edges and curved parts shown in the figure.
Use πr for curved sections where applicable.
Use πr for curved sections where applicable.
5. A circular track has an inner radius of 14 m and an outer radius of 21 m. Calculate the difference between the outer and inner circumferences.
Difference = 44 metres
Outer circumference = 2π × 21 = 2 × 22/7 × 21 = 132 m
Inner circumference = 2π × 14 = 2 × 22/7 × 14 = 88 m
Difference = 132 − 88 = 44 m
Inner circumference = 2π × 14 = 2 × 22/7 × 14 = 88 m
Difference = 132 − 88 = 44 m