Section 4.2 Circumference of a Circle
The distance around the circle is called the circumference. It is the
perimeter of the circle.
The circumference, C, of an circle can be found by using the equation:
C=πxd
C = πd
The symbol, π, is a Greek letter called "pi". It represents the number
3.141592653589.....
* this is known as an irrational number because it is a decimal that ends
and never repeats.
We estimate π = 3.14
Since the diameter = 2 x radius, we can also use the following equation
to find circumference.
C= π x 2r
or
C = 2πr
Circumference, radius, and diameter of a circle are all distance
measurements. Therefore, the units are cm, mm, m, km, etc....
Examples
1.
A toonie has a radius of 1.4cm.
A) Find the diameter. d = 2r
d = 2 x 1.4
d = 2.8cm
B)
Find the circumference (to one decimal place).
C = ∏d
C = 3.14 x 2.8
C = 8.792
C =8 .8cm
2.
Find the circumference.
B)
d=2xr
d = 2 x 1.8
d = 3.6m
1.8 m
1 5
m
A)
d
=
Center
C=
C=
C=
C=
3.
∏d
3.14 x 3.6
11.304
11.3m
C = ∏d
C = 3.14 x 15
C = 47.1 m
A circular swimming pool has a circumference of 12m. Find the
diameter and radius of the pool. Round your answers to one
decimal place.
12 ÷ 3.14 = D
D = 3.82 m
So r is d ÷ 2
R = 3.82 ÷ 2
R = 1.9 m
Practice p 138 #1,2,3,5,6,7,8a
Page 137 Questions 5 and 6 Review
5 A) Suppose you double the diameter of a circle. What happens to
the circumference? It would double!
D = 5cm
D = 10cm
C = ∏d
C = ∏d
C = 3.14 x 5
C = 3.14 x 10
C = 15.47cm
C = 31.4
Doubled
B)
Suppose you triple the diameter of a circle. What happens to the
circumference? It triples!
D = 15cm
15.47 x 3 = 47.1 cm (tripled)
C = ∏d
C = 47.1cm
6.
A carpenter is making a circular tabletop with circumference
4.5m What is the radius of the tabletop in centimeters?
(Hint: 1m = 100cm)
D=C
D = 4.5 ÷ 3.14 = 1.4m
∏
R is 1.4 ÷ 2 = 0.7m
0.7 x 100 = 70cm
Example: From the circle below
Identify 3 radii: OA, OB, OC__
B
The diameter: _AC__________
A
O
C
If OB = 6cm, find AC _6 + 6 =12__
Find the circumference. C = ∏d
3.14 x 12 = 37.68cm
Example: Find Diameter
Example: Find Circumference
D = 2r
D=2x4
D = 25 ÷ ∏
D = 7.96m
D = 8cm
C = ∏d
C = 3.14 x 8
C = 25.12cm