Essential Question Check-In How can you model situations to meet real-world constraints?
9.
Hwttk
Evaluate: Homework and Practice
Find the volume of each design for a box built from a piece of
plywood measuring 60 cm by 180 cm.
x
#5
1.
x
x
x
V=Bh
V= 152.165=37,125 om3
60 cm
x
x
t0OMJOF)PNFXPSL
t)JOUTBOE)FMQ
t&YUSB1SBDUJDF
180 - x
x
180 cm
180 cm
2.
'
T=30
x
Vjstfok
.
60 cm
60=54 ,oo0om3
x
x
l=
Ocm
x
x
x
x
x
30
60
)
T=30
x
© Houghton Mifflin Harcourt Publishing Company
180 cm
3.
V= 30%75=67
,SOOcm3
60 cm
1
x
180 - x
1¥
2
x
¥1
4.
180 - x
2
180 cm
60=1.5×+11
60=2.511
1.5x
36472=62,208
¥5
=
¥
24=X
V=(24'
om3
60 cm
-
24
!
x
Module 20
1.5x
180 - 1.5x
2
180 - 1.5x
2
1062
Lesson 3
5.
A cylindrical candle is to be made from 18 in 3 of wax. If the candle’s height is twice its
diameter, what radius and height should it have, to the nearest tenth?
18=782 h=2dh=2(2D=4r
.4r
Ft!
18=403
Biniradius
6.
ht
.=4.5li
A conical candle is to be made from 240 cm 3 of wax. If the candle’s height is three
times its diameter, what radius and height should it have, to the nearest tenth?
V=5'
240=15026
r
h=3d
KZYCM
h= 20.2cm
trash
'
h=z(2r)=6r
240=203
*¥
radius
3.37
The design specifications for a coffee mug state that it should be cylindrical, with
height 1.5 times its diameter, and with a capacity of 450 mL when filled to the brim.aefullmvgvolvme
What interior radius and height should the coffee mug have, to the nearest tenth of a
centimeter? (Hint: 1 mL = 1 cm 3)
.
7.
⇐ h=t5(2r)=3r
450mL
rzh
-
.ly?=y5Oom3VofV=Tr23rygoom3=3Ir3V=3tr3#zf
3.6cm
3.63cm--r→r=
8.
.
h=2r
Vtztbtm
ttrkr
© Houghton Mifflin Harcourt Publishing Company
r
h
2tr3
3=-3
{
4
9.
h=lO.9om
A bob for a pendulum clock will be a cone of equal height and diameter, made from
3 in 3 of metal. What radius and height should the bob have, to the nearest tenth?
't
.5=Tr3
Flim
.
h=2 -3in
.
Assume a full-grown oak tree requires at least 8 ft 2 of exterior canopy area per cubic
foot of trunk volume. Model the canopy with a hemisphere, and model the trunk
using a cylinder whose height is three times its diameter. What is the minimum
radius of canopy required for an oak with trunk diameter 9 ft? Round your answer to
the nearest foot.
¥ofµ
tNnk9r=4.5ft
¥H*
"5
Module 20
Vanity
h?¥
.
4374T
?
=£4tr2
43741+2112
.PH:546#tft?.8=uFiyMtBft
,7=p
1063
46.8ft
.=r^r=Y7ft
radius of
.
Lesson 3
canopy
10. A mature beech tree requires at least 20 m 2 of exterior canopy area per cubic meter
of trunk volume. Model the canopy with a hemisphere, and model the trunk using
a cylinder whose height is three times its diameter. What is the minimum radius of
canopy required for a beech with trunk diameter 2 m? Round your answer to the
tmkrslm
nearest foot.
h=3H=6m
Bueter
Vtwni
.lk?6#ft.3.20=1Wtft.2
'E4t¥
uthrf
120Mt
canopy
7.FM/gm=radivs
11. Assume a mature sequoia tree requires at least 0.6 m 2 of exterior canopy area per
cubic meter of trunk volume. Model the canopy with a cone whose slant height is
4 times its radius. Model the trunk with a cone whose height is 12 times its diameter.
Modelling What is the minimum base radius of canopy required for a sequoia with trunk
diameter 8 m? Round your answer to the nearest tenth.
W
*
-
-
-
"ails
Yit
:3
6=512+3
-
÷¥ME¥¥r"
°
.
6=307 .2Tm2
12. Assume a mature Douglas fir requires at least 2 ft of exterior
canopy area per cubic foot of trunk volume. Model the
canopy with a cone whose slant height is 4 times its
diameter, and model the trunk with a cone whose height is
12 times its diameter. What is the minimum base radius
of canopy required for a Douglas fir with trunk diameter 4 ft?
Round your answer to the nearest tenth.
128*8*2
.IT?rIano.#307.2t=Hrl4D3O7.2F=4Hr288m=radiusof
.
[*Kee=4as=s
H2=Hft#±
bunks 's .CH?48=6YITft?.2=128tTft?
l28T=Tr( 8D
128ft
8tr2
r=4ft
Module 20
1064
.
radivsofcanopy
Lesson 3
ª)PVHIUPO.JGGMJO)BSDPVSU1VCMJTIJOH$PNQBOZt*NBHF$SFEJUTª.JDIBFM1
Gadomski/Science Source
TH
noni
canopy
2
Howl
review
)
16.e Multi-step A propane tank is designed in the shape of a cylinder with two
hemispherical ends. The cylinder’s height is twice its diameter, and the tank’s
capacity is 1,000 gal. What is the radius of the tank, to the nearest tenth of a foot?
(Hint: 1 ft 3 = 7.48 gal)
-
€D
⇐
Zhenirtsphae
4¥
1000gal
'
¥53.
=
133.69ft ?=V#
,
133.69
r
.tt/!y+r+VhfYFr3B3.69=4tIr3ttftr33il33.69=#tr3.31
1.99€
F-
→
r
2.0ft
.
17. A cylindrical space station is 5 m in diameter and 12 m long, and it requires
0.2 m 2 of solar panels per cubic meter of volume to provide power. If it has two
sets of rectangular solar panels, each 2 m wide, how long should each set of
panels be? Round your answer to the nearest tenth.
Bom
§#s"I÷pa%k→m
.tt#h=ts.m3..z.iaFtmkrPamh
2T#=3Hem=whgth
15t=2(2X)
5%4*+11.8
mlengthof panel
18. Create a design to make a cylinder, including both circular ends, from a sheet of metal
that measures 150 cm by 60 cm. Calculate the volume of your design, to the nearest
extra thousand cubic centimeters.
*
( good for
project)
]¥(
=
fete60 cm
lengthqltfaahastotbasecirok
ex
Base radius
19h25am
Module 20
.
"" 5960=1350014×4×11 .5anp
circumference
.
.
1066
of rectangle
Lesson 3
© Houghton Mifflin Harcourt Publishing Company
boom
V=Bh
150 cm