1. No category

Name
Area of a Circle
R 10.12
A circular bucket has a radius of 6 in. Find the area of the
bottom of
the bucket. The formula for finding the area of a circle is A : ;P. One Way
Another Way
Use 3.1 4 for rr.
Use
A: nf
A: nf
-fx62
:3.1 4x62
:
3.14 X 36
113.O4 in2
ff
With a Galculator
for tr.
Press:
Dispray:
:ffx36
_22,,36
|"
792
_
@mErnm
ffiffiffiffiffi
1
7
:
113.14 in2
The bucket's area is about 1 13 in2.
Find the area of each circle to the nearest whole number.
Use 3.1 a or
!.
4,
r:9yd
5.
6.
r:14cm
7. d :2.4'ft
8.
r:
9. d:8.8m
d:20m
@
O
tc
.o
22 cm
(!
O
f,
!
I.TJ
c
o
@
(d
s)
10.
d:32cm
11.
r:
5.3 m
(L
@
12. Reasoning lf the circumference of a circle is j gn.,
what is the area of the circle?
Use with Lesson
10-'12.
127
Name
Area of a Gircle
P lo-12
Find the area of each circre to the nearest whore
number.
Use 3.1 a or ff.
4. d :14in.
5, r:11.25cm
6.
d:2mi
Brian's dad wants to put a circurar poor in their
backyard. He can
choose between pools with diameters of 15 ft,1T ft,'ar
22ft. Round
to the nearest square foot.
7
'
8.
How many more square feet wourd the 17 ft poor use
than the 15 ft pool?
How many more square feet would lhe 22ft pool
use than the 17 ft pool?
Test Prep
9.
On a water ride at the amuserglt park, a rotating
varve sprays
water for 15 ft in alt directions. what is the ur"u
oi the circulai
wet patch it creates?
A.
(o
o
c
io
30 ft2
B. 31.4 ft2
C.94.2
ftz
D. 206.5 ft2
10. writing in Math Exprain how to find the radius of
a circle with
an area of 50.24 mi.
f
E
c
LIJ
o
6
(Io
@
Use with Lesson
1o-l2.
127
Name
Area of a Gircle
PS I O.72
Pizzena Field Trip As a part of their study on nutrition,
Mr. Johnson's sixth-grade class went to the pizzeriato learn
how to make healthy pizzas.
1.
One group prepared a veggie pizzawith a diameter
ol 2O in. lf the pizza was divided into 8 equal slices,
what was the area of each slice?
2. Another group prepared
a low-fat cheese and
pizza.The
spinach
pizza was then cut into slices
as shown. What was the total area of the pizza?
3. A third group made a whole wheat pizza crust
with a circumference of 157 cm. What was
the area of the crust?
City Map An outer belt is a road that loops around a city.
On this map, Route 936 is an outer belt. Routes 12 and 4
meet exactly at the center of the city.
4.
lf you drove once around Route 936, how far
would you have traveled?
5.
What is the area of land inside Route 9g6?
6. writing in Math Explain the steps you took to solve Exercise 3.
(o
o
c
c
.E
o
f
!
UJ
c
o
o
(g
o
@
Use with Lesson
10-12.
127
Name
E 10,.12
VISUAL THINKTNG
Napoleon's Ghallenge
Napoleon Bonaparte was born in 1769. He became one of the
greatest military leaders of alltime. Napoleon would judge the
intelligence of his lieutenants by posing problems in geometry. The
following problem came to be known as Napoleon's challenge.
The diameter of the large circle with center O is 4 in.
1. What is the area of the
@
o
c
large circle with center O?
2.
Find the areas of the four inscribed circles with centers A, B, C,
and D.
3.
Add the sums of the areas of circles A, B, C, and D. Do they
equal the sum of the area of the large circle?
o
F
6
:
o
o
uI
c
o
a
(!
q)
o
4. Do you think this is true for any size circle in Napoleon's
challenge? Explain.
Use with Lesson
1o-12.
127
Area of a Circle
Find the area of €ach circlo io lhe
Use 3.14 or
Area of a Circle
?.
(9
(:4
LP-)
\---/
\--l
3./ir\
4- d -
14
5 km2
in.
-
Use3.l4fortr.
= 3.14
fet
would th€ 17 ft p@l use
Use 3.14
t"
3oft"
B.
Y:;:: ;l S1!
31 .4
;lprain
tt2
c.
s4.2
#
€ch
1 1
A in2.
circle to tho nmrest wholo number
z
cm2
3' ,'----\
/i\
266 m2
4.t=syd 2ilYd"
6. r-14cm 615 cm2
s. t=2zcm 11520 cm2
ro. d=s2m 804 cm2
-
@zoo.s tt,
how ro nnd the radius of a circre with
Sample answer: BecauseA =
is about
or+.
804
On a wator ride at the amusemsnt park, a rctating valve sprays
water fo.I 5 lt in all dlrections. What is the dea of the circuh;
w€t patch it creat6?
A
*lE
ri
Test Prep
9.
-+x36
-4x@
t1
'/1
153 ft2
use than the 17 ft poo,?
fta
Find tho ar€a ot
50 ft2
8" How mdy more square feet would tho 22 ft pool
cffiE@@
ry:Wmffi
"-''
7
The bucket's
3 mi2
Brian's dad wants to put a circular pool jn thef backyard. He can
ch@e betueen p@ls with djamet66 of 15 ft, t 7 ft, or 22 ft. Round
nea6t square foot.
How many more square
than the 1 5 ft pool?
Witlt a Calculator
-?*a'
x 6,
=3.14x36
=113.04in2
to the
7.
tuother
= 1 13.14 in,
6. d=2mi
397 cm2
Way
U*florn.
One Way
1,764 cmz
5, t - j1.25 cm
Iilin2
nf.
lvhal
because the square root of 16 is 4,
usewinreson
Napoleon's Challenge
is the
s.d=2om
314 m2
7. d=2.4*
5 ft2
61 m2
e. d=8.8m
1r. r=s.3m
88 m2
81n
aEa of th€ circl6?
rorr. 127
E IGI2
vtgual txtiKtilc
Napol@n Bonapade was born in 1769. Ho.became one of the
greatost military leadere of all iime. Napol@n would judge the
intslligonce ot his lidtenants by posing problms in goometry The
following pbblem came to b€ known as Napoleon,s challengs.
ui".i
87 in2
12. Reasoning lf th€ circumfgrence of a circle is l8r.
The diamoter
rcl2
A circular bucket h6 a radius of 6 in. Find the a@ of the bottom of
ih€ buckd. The tomuta for flnding the area of a circle is A ,F.
\-/
1,075 in2
n
nearst whole number
u"..m
r"*. rorz. 127
Area of a Circle
PS
lGt2
Piz€ria Fieid Trip As a pad of thsir study on nutrition,
Mi Johnsn's sixth-grade dN went to lh€ plzeia to lean
how to make healthy pizas.
'I
ofthe la€e circte with cent€r O is 4 in.
.
On6 g@up prepar€d a veggie piza with a diamEter
of 20 in. It th€ piza was divid€d into 8 equat stices,
what
the area of each slic€?
39.25 in2
w
Z
Anothor group pGpared a low-fat chse and
spinach pla. The
wG then cut inio slicos
as shown. What was the total area of the pjza?
pie
About 200.96 in2
3.
A ihird grcup made a whole wheat piza crusl
with a circumfer€nce of 1S7 cm. What w6
the area of the crust?
About 1,962.5 cm2
,{I>t)
w
CiV Map An outer belt is a road that joops arcund a city
On this map, Boute 936 is an oder bett. Aoutes t2 and 4
me€t oxactly at tho cents of the city.
4.
(o
c
l.
io
(!
f
About 37.68 mi
@a of the laqe circie with center O?
12.56 inz
2.
Find the
and D.
5.
3.
(6
(ro
Add tho sums of the
equal the sum ot the
6. Writing in ilath
of the tarce circle?
inside Route 936?
Exptain the steps you took to
$tvo Exercise a
oiameterofsocffi
Yes; 12.56 in2
@
4,
tdd
Sample answer: I divided 157 (the
circumference) by 3.14 to find the
are6 of circlesA, 8, C, and D. Do they
ea
What is tho area of
About 113.(M mi2
ares of the four inscribed circl6s with centers A, g, C
All of them are 3.14 in2.
uJ
@
What is the
lf Wu drove once arcund Route 936, how far
would you have travelod?
Do you think this is true tor any size circle in Napoleon,s
challonge? Explain.
$ample answer: Yes, the relationship
qftlre circles stays the same.
usewnnressonr+rz.
127
diameter to find the radius of 25 cm.
The!, I useA tne tormuti tor area to
us"*uem'rorp. 127
Use with Chapter 10, Lesson
12 127