Circumference = πd = 2πr

```G.GMD.1 STUDENT NOTES WS #1
1
Dimensions are important to understand in this unit. As we progress though the dimensions our units of
measurement change. So for example, the items that we measure in one dimension are perimeters,
distances, and circumferences. All of these are lengths and exist in one dimensional space. In two
dimensions, we move into area and square units we begin to measure the number of square units within the
shape.
ONE DIMENSIONAL MEASUREMENT
POLYGON PERIMETER
Perimeter refers to the distance around the edge of a closed figured shape. Perimeter formulas are often
quite simple because they sum of the sides of a polygon. In some figures we can create condensed forms of
this relationship because of the side properties of the polygon.
Square
Rectangle
Triangle
Regular Pentagon
C
w
d
l
P = 2l + 2w
S
b
D
c
B
P=b+c+d
P = 4s
S
P = 5s
CIRCLE PERIMETER – CIRCUMFERENCE
The perimeter of a circle is called its circumference. The circumference of a circle is the distance around the
edge of the circle or in other words, the arc length of the circle. To discover the circumference formula we
need to look at the relationship between the diameter and the circumference. The ratio between these two
values will reveal one of the greatest numbers of all time, π.
d
d
d
d
d
d
d
d
?
?
Notice that each time we get just over three diameters. It was this pattern that led many to explore what the
value was. The history of pi is a great historical topic to study and if time permitted I would strongly suggest
you investigate it further. We learn that depending on the culture and the time
period pi has received different approximate values for its irrational value. The
ancient Babylonians use the value of 3, while the Egyptian Rhind Papyrus notated
pi to be 3.1605. Archimedes of Syracuse (287-212 BC), one of the great Greek
mathematicians using regular polygons to approximate a circle was able to narrow
down the value between 3 1/7 and 3 10/71. As time continued many
mathematicians were able to establish ways to determine more and more correct
digits of pi, for instance by 1699 the first 71 digits had been calculated correctly.
Determining of digits of pi was a mathematical pursuit by many great scholars.
Again this is a fascinating history and it would be a nice exploration.
Circumference = πd = 2π
πr
G.GMD.1 STUDENT NOTES WS #1
2
Determine the missing information.
C = 9π cm
r = 16 cm
r = 3 cm
C = π cm
r = ____________
d = ____________
C = __________ (E)
d = ____________
d=9
r = 4.5 cm
d = 2r
d = 32 cm
C = 2πr
C = 6π cm
C = πd
d = 1 cm
Determine the perimeter of the given shapes. (Lines that appear to be perpendicular are perpendicular.)
8 cm
10 cm
2 cm
6 cm
11 cm
18 cm
8 cm
P = 11 + 8 + 2 + 2 + 9 + 6 = 38 cm
62 + 82 = x2 x = 10
C = ½ πd = ½ π(8) = 4π
P = 18 + 6 + 10 + 10 = 44 cm
P = 8 + 4π cm
G.GMD.7 WORKSHEET #7
Period
that no matter what size of circle you will always have 6 and a bit radii that will fit along the
circumference. Lenny disagrees he says that if the circle is really big then more than 6 complete radii will fit
along the circumference. Who is right and why?
k-l- } -(
<-t ; o-"-*'
u,r.- {t{4t--{.- l'
1. Jack says
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ul't"-
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11,
a
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2. Pi is an irrational number. What is an irrational number? Give another example of an irrational number.
3. Determine the circumference. (E) means leave as an exact value.
a)
c
r=3cm
=
L.
-tr
t"yw'
b)
d=B.5cm
(E) c -
c)
r=5..6
d) d =
(E)
(E)
5
-cm
4
f=
(E)
4. Determine the missing information.
a)d=3cm
b) C = L6n
cm
c1, =
g
!.*
d)C=5n
= hf"r "'''
tt'--'
-L-
cm
1E1 r =
.L
5. Archimedes estimated the value of pi in 230 BC ,sine &rTai'folygons. While this is not the method
that he used, we will also use a regular polygon to approximate the value of pi.
The perimeter of the regular decagon is a close
approximation for the circu mference.
a) lf the side length is 6 cm, what is the perimeter of the
regutar
decagon? L (p\
Perimeter
= 6c fri't
b) Use trigonometry to determine the radius of the regular
polygon.
(4 decimal places)
Diameter =
(4 decimal places)
c) Now divide the perimeter by the two times the radius to
see how close our approximation is for pi.
/"",c
['(.t'!tt"i
Approximation for pi
=
J .Cq {*u(2
decimat ptaces)
-72
4'L*l
G.GMD.I
WORKSHEET #7
2
6. Determine the perimeter of the following figures.
(Lines that appear to be perpendicular are perpendicular.)
b)
a)
d)
c)
I (rti
3 en:
l
,6
(rY1
Scm
Circumference
Perimeter = X-L tvq
Perimeter
e)
f)
= iz't( t wr
=
Perimeter
(E)
=
h)
s)
lO crn
2cm
Circumference
Perimeter =
(E)
=
i)
1O
m)
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U
r {Arq
i
{-rlt1
cnl
Perimeter =
rrn
n)
?i
l-S cn"
(E)
r&1 rzrL
Perimeter
=
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Perimeter =
*u\
(E)
o)
'-"'"
10
{m
L-
30 t*
Perimeter =
Perimeter
:"fi"
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4cm
=
Perimeter
C
tA {fi1
l0{ffi
= {t;
=
'L'8
k)
i)
Perimeter
Perimeter
(E)
Perimeter
=
luF* &a cui,t g)
loof 5a't9!
G.GMD.I
WORKSHEET #7
3
7. Determine the perimeter of the following figures.
(Lines that appear to be perpendicular are perpendicular.)
+(.1+t{}-ls+tfir) J
+ s.JL + K-.(r )
Ll
b)
5cm
dl"l
a-
,5
rm
Af f U (1 Y- I [/
=
perimeter
= bfl tT
c,tt1g1
Perimeter
n
G
d)
a
a t1 vZ
I r-(r)
6r+'lvz
Perimeter
=
(L dec.)
=
5(m
6Xt q fZ t'\E\
Icm
Perimeter
(E)
=
e)
*(rn rcrn
*i j*,
\$tm
Perimeter = 1
r-#
rrF c'"fA,
Perimeter =
(E)
```