Page 77 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

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ler and two set squares to t distance across the circle.
t squares rest squarely on
istance across the circle. eussttotakethiTshinetvoaalucecoufn􏰀tis3.1415926535....
EXAMPLE 1
The value of 􏰀 is 3.141 592 653 5....
􏰀 is an irrational number as it is neither a terminating nor a recurring decimal.
ay need to start your
Example
Exerc
1 Ca th
(a)
2 Th 15
ThFeovraelxuaemopf l􏰀e:is 3.141 592 653 5.... es to The value of 􏰀 is 3.141 592 653 5....
and two set squares to rom a calibration that is
circle. 1 1 Find the circumference of a circle with
􏰀 is an irrational num2ber as it is neither a scuircelet.he diameter.
m a calibratiFoonrtehxatmisple: r
Use 􏰀 = 1 d.p.
t is
st take this iFnotroeaxcacmoupnlet:
To simplify calculations, you 22
t is count
1
1 – usually take 􏰀 as –– or 3.14.
re the diame2ter.
– = 0 5 (terminating decimal)
􏰀 is an irrational number as it is neither a
quares rest squarely on terminating nor a.recurring decimal. 􏰀 is an irrational number as it is neither a
y on terminating nor a rec1urring decimal. (a) diameter 21 cm
y need to start your –3 = 0.333... = 0.3 (recurring decimal) y on terminating nor a recurring decimal.
r
For example:
22 –– 7
C
= 0 5 (terminating decimal) – = 0 5 (terminatin2g decimal) 7
(b) radius 2.8 cm. and give answers correct to
2 The circumference of a circular swimming EXAMPLE 2
count
6 7 8 9
ndthelenguthsuyaolluyrteaqkuei􏰀rea,s––or3.14. C
–1 = 0 5 (terminating decimal) .
. 1
2
1 – The formula for the
= 0.333... = 0.3 (recurring decimal) – = 0.333... = 0.3 (3recurring decimal)
O
3 . circumference –1 = 0.333... = 0.3 (recurring decimal)
pool is 28.3 m. Find:
3 To simplify calculations, you
d
To simplify calculations, you 10 11 12 13 14 C
(b) its radius.
Use 􏰀 = 3.14 and give answers correct to
22––
usually take 􏰀 as or 3.14.
Tosimplifycalcul–a–tioSnins,cyeou=􏰀
usually take 􏰀 as or 3.14. 7 C
C
7d 22
(a)
3
22
(a) its diameter
7The formula for the
Then C = 􏰀d (Multiply both sides by d.)
surements? The formula for the O
circumference O 1 d.p. The formula for the d
circumference e circle. Whcaitrcduomesfetrheins ce
Od
The formula for the circumference of a circle
7 8 9 1011121314C C d
t? Since = 􏰀 Sininceterm= s􏰀of its diameter is: 1 (a) Given that d = 31 cm and 􏰀 = 22 , the
Cdd –– the length you require, 7
quire, Since d =􏰀 C=􏰀d circumference of the circle is C = 􏰀d =
Then C = 􏰀d (Multiply both sides by d.) ritehmyeonutsr?otheTrhoebnjeCct=s.􏰀d (Multiply both sides by d.)
quire, 22
–– × 21 = 66 cm.
sults in a tabTlehelinkeCth=i􏰀s.d (Multiply both sides by d.) 7
hfeirsence, Diameter, C
circumference of the circle is C = 2􏰀r =
in terms of its diameter is:
The formula for the circumference of a circle
circle. What Tdhoesfothrmis ula for the circumference of a circle
his Making d the subject of the formula
22
(b) Given that r = 2.8 cm and 􏰀 = ––, the
4 Th is
do on w
5 Th tra
(a)
Us
6 Th lin
th th
(a)
(b) (c)
Ta
in terms of its diameter is:
The formula for the circumference of a circle 7
in terms of its diameter is:
d C 22
d
Show that the diameterSohfoawcitrhclaet d =
C = 􏰀d 2 × –– × 2.8 = 17.6 cm. 7
your other objects. C = 􏰀d 􏰀
s. C = 􏰀d ts in a table like this.
s. is.
2 (a) Given that C = 28.3 m and 􏰀 = 3.14, is. MaEkxinpgredsstihnegstuhbejceicrctuomftfheerefnocrmeiunlatermsofthe
Making d the subject of the formula
the diameter of the circular swimming
ence, Diameter, C radius
C Making d the subject of the formula C 28.3
mference d d C pool is d = 􏰀 = Cd C Show that d =
3.14
= 9.0 m (1 d.p.).
Show that d = Each diameter of a circle is made up of two d C􏰀 􏰀
Show that d = 􏰀 radii in the same line. Or:C = 􏰀d
Expressing the circumference in terms of the
Expressing the circumference in terms of the
So the diameter of a circle is twice its radius.
28.3 = 3.14 × d ference radius 28.3
radius
, what did yoExupnreostsinceg the circumference in terms of the
t when you rdaidviiudsed the Each di=amr ×et2er of a circle is made up of two = d
hen you divided the
d = r × 2 So C = 2􏰀r
henece of a circle
d = r × 2 􏰁3
diameter?
here of a circle d = r × 2
􏰂 d = 2r
The formula for the circumference of a circle
Each diameter of a circle is made up of two
radii in the same line. O
he diameter? rad􏰂ii din=th2re same line. Each diameter of a circle is made up of two
radii in the same line.
d = 9.0 m (1 d.p.)
uld have shown that: SoStihnecediCam= e􏰀tder of a circle is twice its radius.
So the diameter of a circle is twice its radius.
C
C
Sorthe diameter of the circular swimming pool is 9 m.
C
hat did you notice Then C = 􏰀 × 2r
So the diameter of a circle is twice its radius.
3.14C
means ‘is ap􏰂prodx=im2artely ld have shown that:
Since C = 􏰀d
t: t:
Since C = 􏰀d Since C = 􏰀d
O
in terms of its radius is C = 2􏰀r.
r C
28.3
2 × 3.14
􏰂 d = 2r
(b) Given that C = 28.3 m and 􏰀 = 3.14, the O radius of the circular swimming pool is
ceofacircle ThenC=􏰀×2r Then C = 􏰀 × 2r
Then C = 􏰀 × 2r O r
r = Or:
= 4.5 m (1 d.p.) 28.3=2×3.14×r
of a circle 􏰁So3C = 2􏰀r So C = 2􏰀r
So C = 2􏰀r r
Making r the subject of the formula
y the Greek letter 􏰀 (pi).
􏰀 (pi). (pi).
C Show that r = Show that the radius of a circle
C
2􏰀
So the radius of the circular swimming pool is 4.5 m.
2􏰀
in Stherow that sr r=adius is C = 2􏰀r. Theformulaforthecirc nceofacircle
=
The formula for the circumference of a circle abnys t‘hiseaGpprereoTkxhilmetfatoetrerml􏰀yu(lpai)f.or the circumference of a circle
C = 2􏰀r
tely ely
C
in terms of its radius is 2􏰀 in terms of its radius is C = 2􏰀r.
28.3 = r 2 × 3.14
Making r the subject of the formula
Making r the subject of the formula
Making r the subject of the formula
r = 4.5 m (1 d.p.) 339
Show that r = 2􏰀
Show that r =
. . .
C
2􏰀
ms of it
umfere
C = 2􏰀r.
340
339
339
71
339