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Quick Review
The distance around a circle is its circumference.
The ratio of the circumference, C to the diameter,
d, of acircle, f, is a constant close to 3.
That is, the circumference is approximately 3 times
the diameter, or 6 times the radius.
The Greek letter
"C
IOr
t
is used to rePresent the constant
7.
Insymbolsrf,=n
n is an irrational number
An innoiionol nornben
equal to about 3.14.
is o
decirnolfhof
neven nepeofs ond
So, the circumference,
C is n multiplied by d.
never tenrninofes.
C= rrd
Since
d=2r,C=tt x2r, or C=2tr
diameter or radius, and vice versa.
The table shows some examples.
r:
Approximate Value (for
Distance
Formula
Radius
r=Td
5m
1.5 cm
Diameter
tC
a=;
10m
3.0 cm
Circumference
C=rrd,C=2tr
31.4 m
9.42 cm
3.14)
I
l.
Estimate the circumference of each circle with the given diameter.
a)
2cm C'nl
7xZ -' 6.**
Use
Tr=3for
estimotes.
c)4.2m 4= nA
L=n&
7Yz1 =J/-c-tw- Zxq- z = l2-6
b)24cm
*--)
@*
'\w
125
2.
Estimate the circumference of each circle with the given radius.
a) 2 cm
c=ftd
3'
J=
bl 24cm
e{cyu!-
?xq:
J= {8.,.-
c) 4.2
(Zcv,,^.- 3x.rb = tqttcu,^
A
m
3x 6-y
= 8.{
2€-7 t+
calculate the circumference of each circle in question 2.
Give the answers to the nearest millimetre.
a) r=2cm
b) r= 24cm
(= nJ
C=
r=4.2m
FtJ
c.n
3.tt x 4E . rf,o.72c'*
3.lLl X a1= lZ.SLervl7.L etv-
lSb.7
3.ttx
J
6..{ = 76.32
c.,r^-
a)
d= 3.18.,-
b)
r= l.Stt.^-
d= n'71 c'*-r* 4-aLcv*
cl
d-
lL.l o r'*,,r^
r=
(.ofr.,^.,a-
5. A glass has a circular base with a circumference of 2r.4 cm.
a) Calculate the diameter of the circular
base. 6 .8 I .t^-
b) Circular coasters are made to extend beyond the edge of the glass base by
I cm.
What is the diameter of the
coaster? 8. t f
c) Calculate the circumference of the coaster.
c rn^
7a. ( 6 <.v\_
6. A car tire has a radius of 36 cm. A stone gets stuck in the tire. How
many times will it hirt
ttt:g{ when the car travels a distance of I km? show your work.
(= nJ
)2: /ZL-vrt
= 2-26 vv..-=3.1H x
The stone will hit the ground
I b.^ t
lsqua^I ss q a 2. LU
Cincornfenence is fhe
disfonce oroord fhe
con fine.
L
26.4 vn
4. Calculate the diameter and radius of each circle.
Give the answers to the nearest millimetre.
126
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,n-