Gr.7 Volume of Right Prisms

Unit 10
Grade 7
Volume of Right Prisms
Lesson Outline
Sig Picture
Students
_ develop and apply the formula: Volume "'" area of the hue x beight to caleulate volume of right prisms;
• understand the relationsbip between metric units ofvolume and capacity;
- understand that various prisms have the lWne volume.
EXI,loring the Volume
ofa Prism
I_
2
i Metric measures of
•
Volume
not inc'fu"fed)
•
•
Metric Measures of
Cal'llciIY and Mass
•
not ifl{~tu,rJe,ij
(See Metiic Cal)lu.~ity
and Mass-My
Professional Pr14ctict>:)
Volume ora
Rectangular Prism
•
•
•
•
5 IVolumeoh
Trimgular
•
•
Volume ofa
Prism with a
Parallelogram Base
7
Volume ofa
Tmpezoid"Based
Prism
•
•
•
•
RelMte exrnmential notation to vOlutne,
cubic units.
Determine the number of cubic centimetres that entirely fiU Ii
cubic decimetre, e.g., Use centimetre cubes to determine the
tbe base. How many layers are needed I COE 3b, 4a
number ofem' that
to fiU the whole
Determine how many dm3 fiU a and use this to determine how
many em' are in iii m3•
Solve problems that
conversion between metric units of
volume,
EX1::llo1re the rel.ationship between
and littell, e.g., cut 11 2·titre!
1m42
carton horizontally in half to make il. l·litre container that
measures 10 em x 10 cm x 1() em, This con.talner holds 1 litre or I COE 3b. 4a
1000
Determine that 1 em:l holds I miUilitre.
Solve problems that require conversion between metric uni.ts of
volume and capacity.
Determine the volume of a rectangular
Volume area of the base x height
Solve o[ohlemll involvim~ volume of a
using the formula
Determine the volume of a triangular prism, usinR the formula
Volume area of the base x height.
Solve problems iuvolving vol.ume of a mmgular prism that
conversion between metiic measures of volume.
Determine the volume of a paraUelogmm-based
methods.
Determine that the volume of the paraUelogmm·based prism em
be calculated,
the formula: Volume '" area oftbe base l(
height.
Solve problems involvinl! volume of a
prism.
Determine the volume of a trapezoidal·based prism.
Solveproble.ms involving volutne of a trapezoidal-based
7m34, 1m40. 7m42
COE4b,4c
7m34, 7m40, 7m42
COE
Sd
7m42
COESf
7m23,7m34,
1m40,7m42
COE5f
TIPS4RM: Grade 1: Unit 10 - Volume of
Prisms
1
8 IVolumeofOtber
Pristm
9
Linking Surface Area
andVolurne
,_
-
Surface Area and
Volume of Right
Prilltm
-
•
Determine the volume of right prisms (with bases that are
pentagons. hexagons, quadrilatemls, compollite fifgllfeEl),
methods,
7m23,7m34,
7m40, 7m42
COE3b
Apply volume and area formulas to expl.ore the relations.hip
between trianlrolar pris.ms with the same surface area but different
Estimate volumes.
Investipte the
rectangular
7m42
COE4e,Sa
between surface area and volume
7m42
st!J<ients' kltWWle(ij~e and understanding ofvolume of
with
bases,
COE3a,3c
Skins test
3c
TIP$4RM; Grade 7; Unit 10 - Volume of Right Pri$!ml
2
Unit 10: Oal1:. EX~lorini the Volume of a Prism
Math Ltarnfog G911!
era. 1
MSt!1lt'
Rel~te e~ponential
.. Develop and apply the formula for volume of a prism, Le., area ofbue x: beight.
..
notation to volume, e.g., explain why volume is meli$ured in
cubic mUt!l,
•
•
, _.....
A
•
• U;O,,_u.1: uO,
paper
(BLM
Assessment
.
Mlnd1iiOn...
~()~~.
• linking cubes
•
,21(U.l,
Whole Cllsa :Z euided Instru!tti9D
Show a cube and uk: If the length ofone
~ area ofone face? (I
.. What is
unit')
I unit:
has at least
of
.. What is
..
..
is area
is
congruMt, paratlel
in l'iYt,,,,,,,, ,.ntt,,?
measured
lead students
UlrOu2h a
Count the cubes to determine tbe volume ofthe
•
Actionl
Paifl.:Z lov!tt'gmlgo
Invite students to li$K: clarifying
Students create several more irregular
displa.y
Building Towers,
about the inv~tigation
of various
the table.
saulP1cls, state a
fomrmla for
the volume
Volume afea ..Ube base x height
Students test their formula for accuracy by constructing two other towers.
Curriculum ExpeetadouslOral Questioning!Anecdotal Note: Assess students'
formula Volume area of the base
•
Consolidate WholtClaa,:z Student
Debrief
As students
their
Pre,eotiltloo
fwtlingis, surrnnanze the r~ults
of the
on a cla.'ls
chart.
cOfl:lPlete ll. few examples,
calculating the volume fit ."M<tm"
[?.
10_
fl
a diagram.
Reinforce the concept ofcubic units.
II stlJdenbii Ullfl
decimal and
!'malenal measures,
an infinite number
prisms is ~~"UJle.
TIPS4RM; Gmde 1: Unit 10 - Volume of
Prisms
;3
10.1.1: Building Towers
Name:
Date:
Each tower pictured here Is a prism. Build each prism and determine the volume of each
building by counting cubes,
Tower A
Tower
e
Tower C
1, Complete the table of measures for each tower:
2. What relationship do you notice between volume, area of the base, and height?
)C
(eo..
Ira-
:;
lu~
3, State a formula that might be true for calculating volume of a prism when you know the area
of the base and the height of the prism,
4, Test your formula fo·r accuracy by building two other prism towers and detenmining the
volume, Sketch your towers. Show calculations on this tabia,
o
E
Explain why your formula is accurate.
TIPS4RM: Grade 7: Unl110 - VOlul'I'le of Right Prisms
4
_
Minds On".
Whitt CM!S =t IbJring(pi'5¢YHlon
Students !ihare their di~ aOOllOlutions for prisms with a volut:ne of24
Students build ~ with
cubes (assume the prisms are usmg
jn~~gel;djlnetlSj<>ns). Relate
to the
of24.
concrete
reetmguw prism, askltrldents:
vohune the mne or differoot whoo the primm are ()riootoo vertiC€lUy
or h<>rimntalny?
• Is the base
rectan.IitU~1lf
• What do we mean bv "dimensi,O'rIS
_Actionl
For any prism:
V '" ~ of l::ltie x
hetght
For I'l!ICtangular
h
Whoo calCUlating
volt.I!'M of a
r~lngullar prl$m,
any
can
be thought of li$ hi
baH.
Pitt! =t Investt.ion
Students use a re<:tanlu1ar prism to sbO'w that
vollumlC. Tlmlilins the same (based on the ~ml
of V<>lut:ne area ofthe
base'l."bey invesligate how to use the formula to calculate volumes of
several examples ofhonzontaUy lWU
oriented prisms, lWd show their
tbeir conclusi<>tls.
Curriculum ExpectationsfOral Questioning!Anecdotal Note: Assess students'
area of the ~ x
_
Con~oildate Whole Class • ~ .R~fle~ion.
Debnef
Students share tbelt mvestlllltlOn ,,"u J""''''J
and calculations.
Hc;>me Activity or Further Classroom Consolidation
• Make two or three sketches of rectanguw prisms with whole number
dimensiom with volm:ne:
Pr(1{';twe
ll) 27
.48
are there
ofvmume48
tban21
•
that can be gooerated several
•
a volm:ne
_
differoot sets of 1:ne1lSUret1llelllts
whole
dimoosions. E7q,laiu.
'" Lommere the
Provide students
appropriate
practice questloos,
practice ques1tiolllS.
T!PS4RM: Grade 7: Unit 10 ~ Volume of Right Prisms
5
----J-H~-
- ---_.-
Grade 7
j""...".. . ,., . ;;
;0,.....'.....:. .
AueS$ment
Opportunities
•
Mind$
For any pmrm:
V'" .,..ofbau x
height
for triarlgtlIar
prlsrm:
v'"
tbhx H
make
tmmgkM. no! OM of
the~,
•
Some I'lt1ldant$ may
need the phy$ieal
I'Ill:ldeI to lilMlfrt their
Action!
l.lfldfmtl!lnding,
Curriculum ExpecrationslOral QUC8tioningiAnecdotSll Note: Assess stu<ienIS'
formula Volume
woon uaignlng
trtaflgl.dar prism
•
ConsoUdstG
Debrief
rlh!?', Cla$' -+ Rdectign
Students share their investigation fin.iinfi&S,
ident!j'v tl1e triangular face as tbe
~$froma
textbook, eI'l$Ul'a
that no QWSt!ol1$
require
URof
the Pythegoreal'l
Ihaorem,
Home AetlvlW or Further Classroom Con$olldatlon
Sketch llnd label the dimensions of a triangular prism whose whole number
Practice
pmduc:e a volume that
a) an even tltuni'llt':r
an
number
c) a decimal value
c"'P....u
your
in each case.
T1PS4RM: Grade 1: Unit 10 - Volol'l'1e of Right Prl$ffi$
6
10.5.1: Volume of Triangular Prisms
Show your work using good form and be prepared to tell how you solved the problem.
1. Determine the volume of the piece of cheese.
Create a problem based on the volume.
Picture
Skeleton
H:::; height of prism::; 5.0 em
length of rectangle::; 6.3 cm
Base
height of triangle::; 6.0 em
base of triangle::; 4.0 em
2. Determine the volume of the nutrition bar.
Create a problem based on the volume.
Picture
Skeleton
Length of rectangle::::: 5.0 em
TIPS4RM: Grade 7: Unit 10 - Volume (If Right Prisms
Base
D
Equilateral triangle with:
height::::: 3.0 em
base::::: 3.5 em
1
10"5,,1: Volume of Triangular Prisms (continued)
3. Determine the volume of air space In the tent.
The front of the tent has the shape of an Isosceles triangle,
Create a problem based on the volume.
1.6m
4. al If you could only have 1 person per 15 m3 to meet fire saf~ty standards, how many
people could stay in this ski chalet?
,!Hint;
'Think about whether the height
,of the chalet is the same as the
height of the prism.
Which measurements are
unnecessary for this question?
5.0m
Height of chalet Jt;; 7,1 m
b) How much longer would the chalet need to be to meet the safety requirements to
accommodate 16 people?
TIF'lS4RM: Grad~ 1: unit 10 - Voluml:l of Right Prisms
8
•
•
..
M$HSment
2: RIMoMtr!tlon
Display two triangular prisms with congruent
e.g•• use polydron materi.als
two triangnlar prism chocolate hars. Of two triangnlar prisms cut fmm the net on
SMlngtMtwo
BLM to,6d,
together to l'l'lilIke a
Students ~ure and calculate the volume of one of the prisms. Demonstrate how
p:I'Ism am help
Minds Ort.. , !thole Clm
lht """
priams "'" be_ togetber1D ~
trlMgutar pl'lSl'Nl
~tlyfltted
p$l'8lletogrlllm-bued
~.l.\allze
tl'lev~lI~
and bUild
.Actionl
Two~:
Pain!~Jnvestigatjon
How can the volume ofthe parallelogram-based
to the
he determined. knowing the volume of one triangnlar prism?
find a
method for calculating the volume of a parallelogram-based
prism and compare the two methods,
that their findings are
true creating several other
paJll11jelo1~n-tr.:ll«ld prism ~urements.
The volume of a parallel~-hal«ld
can always he determined
de<;oml~iing it into two triangnlar
formula Volume"" area ofbase x
detentdne the volume
Students
•
ttl.,.
a) Multiply the
triangular prism's
volumeby2
b) Use the volttn'le
formula: eres of
the base )( height
Consolidate WhOle Cliss ~ Oi.fCY$sl9!!
Debrief the students' findings to help them understand that the volume of a
can he determined by determining the area ofthe
which is conwol«ld of two congruent tri.angles and is (b x h)
The vohtme of the pat'all(~h)lJrlll:n-t>as(~d
prism can also he determined
the formula:
Volume "" area of the base x height of the prism.
Debrief
Model the solution to an everyday problem that requires finding the volume and
caplacilty of a paraUelogfllln-based
Home Activity or Further Classroom Con$olldallon
• Write a paragraph in your journal: There ill one formula for all
is, .. Here are some
ofhow it is used.. "
OR
t:xpedatmns!
Demonstration!
Martd:ag Stlmne:
sIDdenl,'
• Complete the practice questions,
TIP$4RM: Graoo 1: Uni110 - Volume
It
Prisms
understalldiol,l of the
fot
9
...
o
*' •
Unit 10: D~y 7: Volume of Trapezoidal-Based Prism
•
•
Grade 1
Mlth be@rnlno GgIII
• Determine the volume of 11 trapezoidal-bued prism using several methods for
,,<ti.... t'l- formula Volume "'" area ofthe base x height to determine if there is 11
•
•
MettrJIlI
.13LM 10.1.1
pm,blems involving volume of it trapezoidal-based prisms.
)\ssessment
%R!Vlm
Review the definition and characteristics of a trapezoid. Recall methods for
calculating the area
trapezoid.
MindS On•. , Whole CIM.
Actionl
eai[l :% Investiglt.9D
Students complete the investigation:
Can the formula Vol.ume area of the base x height ofthe prism be used to
determine the volume of trapezoid-based prisms instead of decomposing the
trapezoid?
InvestiiBte to determine the volume of a trapezoid-based right prism by
dec:om.posing the trapezoid into
and rectangles, using different
Students l'Il8Y
~todothe
Olilleulatlons u$log a
2-D dltltgram of the
~.Other
~l'Il8Y~
to bl.tlld the 3-0
~
to vlfwalla
the &Olutioo.
Compare the solutions from the decomposition method to the volume calculated
using the standard formula.
Write your
in a report Include
and calculations.
Prompt students who are having difficulty decomposing the trapezoid
SUi~gestirtg some of these possibilities:
Problem Solvlng/AppUclltion/Checkbric: Asses students' problem
tec:hnlqules, as well as their communication in the report.
•
ConsQlldate Whole Class ~ OI!Stussion
Debrief
Practice
DillCuss the need for h and H in the formula and the importance of the order of
Focus the discussion on the fact that the standard formula Volume area of the
base x height of the prism always works for right
Volume can also be
calculated by decomposing into composite
V "" area of bas£~ x. height
Ol"der of operations
V""
is important to
Olillculale ~y.
Home Activity or Further Classroom Con.solidatlon.
Complete worksheet 10.7.L
TIPS4RM: Grade 1: Unil10 - Volume of RighI Prisms
11
10"7" 1: Designing a Box
A local pet food company wishes to package their product in a box. The preliminary box design
Is shown on the left.
acm
pet
f~
9cm
Box A
BoxB
1. Determine the volume of the box on the left Verify your calculation using an alternate
method.
I~
c::.
_
reo 0
o
1<."
I"t\
s.
ern
'a>
12CHI't!.
'l.. \{
'Ie
em
2-
2. Box B has the same volume as Box A. What is the height of Box B1 Explain how you know.
1"1f'I.'Z..
is ,""
1"1"...
same volume as the two boxes above.
Alternate
Build Box A and B. Be sure B has the same volume as A. Fill them up to check for equal
volume.
TIPS4RM: Grade 7: Unit 10 - Volume of
flrl$ms
12
Grade?
Mltldlll
• BLMlO.IU
A$$ft$ment
•
Minds On...
lingI! klsl- 7 f!ref!nmt'iDl
Students di~s the solution tbe homework problem. Some students share their
design for Box C. The
the dimensions for correctness.
If students built Boxes A and B, have them
their tnethod and prove that
tbeit volwmes were the same•
•
Action!
WboleC'na7
Use a mind map t o a
of other
that could form the
base
right prism.
Students sketch the 2-D
on the board pentagons, hexagons, quadrimterals,
OOttlPOl>ite figures..
Have ~ of the
I con~ lIoures
avaitable fot student
I'IIlfer~.
CompoMe
for the base
priIml.
[,earnillg SldIls (ClassPartieipation)!Ob!iervlltiouIMeutal Note: Assess
students'
durin$!; the brainstorm.
Plt£!:tP~
Students decompose tbe
disculiS how
would
calculate the volu:me of that
into
mo rectangles. They
the area of tbe
of the bue in order to
V"" area of bue x
the
and rectangular
Pli£!:t Probllm§olvlns
Students complete BLM 10.8.1.
•
ComJolldate Who'! ~ll$a :t. Prelentation
Debrief
Students present md explain their solutions.
Home As;tivitv or further elYlroom Consolidation
Practice
Design two right prisms with bues that are polygons. The
approximate capacity of 1000 mL
TIPS4RM: Grade 7: Unit 10 ~ Volur'lUil of Right Prisms
must have an
13
10..8.. 1: Designing a Gift Box
Determine the volume of the gift box designed by the students from Trillium SchooL
Shape of the base of the box:
Skle view of the box:
10 em
Scm
Volume of the box;
': I 'l:: w...::>
\ :
':;.
::::
':::.
c~
:;:
Ic.m.~:- ll""i""'\\
Capacity of the box;
,
em
TIPS4RM: Grade 1: Uolt 10
Volume of Right PrlSrNl
.~
m'
14
Unit 10: Dar 9: linkins Surface Area and Volume
.
.
Grade 1
Math yarning GOIII
... App··.I.Y .V.olnme.. a.M. area fonnulas to explore the relationship between triangular
pOsml> with the nme surface area but different volumes.
... Estimate volumes.
M'wrtm
• r.. ecmn
•.•..gular Wp 0.r
sheet
.
• connecting cubes
• BtM U.t9.1
•
Assessment
•
GrO"111 ~ Oiscu!slqnlPresentdOo
Students share solutions for homework questions assigned on Day 8 for volume
prisms with polygon
Each small group presents one solution to
the whole class.
Minds On... §ma,1
Whole 'IRS ~ Investigat"2"
Place a large
on the floor/ground. Invite six students to become vertices of
a trianf:!Ular nrism tent Four of the students are to
their vertices on the
stand 00 the comers of the tarp. The remaining two students stand
on opposite sides of the Wp. equidistant from the ends. to beeome the fifth and
sixth vertices. These two vertices gradmlUy raise the tarp until a tent is furmed.
Note that the
vertices have to move. Invite two or three other students
to be campers.
Smderl.ts verbalize observations about the tent's capacity as the tent's height is
increased and decreased. Ask: Does it feel like there is more or less room.?
Pail'$ :2 Mooerl Making
Students simulate the tent experiment using at sheet of paper and connecting
cubes. Data maybe collected in a two~colunm chart height of the tent vs.
number
cubes that will fit
the tent without bulging the
sides.
•
Actlont
•
Con$olidate ThinkJPalr/§hare 2 Discu!sion
Debrief
In pairs, studerlts respond to the
Is the foUowjmt statement
or never
Two
prisms with the same surface area also have the same VOlume,
Ask probing ques.tions to e~ that students realize that investigation of this
statement differs from the terlt
since the floor and the triangular
sides were ignored in the terlt scenario. but cannot be iguored in this question,
Ask studerlts if their conclusion would be the same for closed and open~erlded
Who.! Class :t Rl!c"!ssim
Discuss how an experi.merlt might be designed to confirm or derly hypotheses
about the relationship between surface area and volume,
Home ActM~or Further Classroom Consolidation
Skill Practice
On worksheet 10,9.1, make two folds using the two solid lines. form a
Imagine that it also has paper on the two trian.gular erlds.
and jts net. Take the metdSurements needed to calculate the
area (inClUding the two triangular erlds) and volume, Label the
diagram.<; with the measuremerlts. Calculate the surface area and volume.
Repeat the process for the prism formed using the two broken lines,
Make a statement rell:ardina your findinll:s that relates surface area and volume.
TIPS4R.M: GradEl 7: Unit 10 - Volutml of Righi Prisms
This activity might be
done~orlna
g~m.~
u&lng afope to hold
tNi peak of the tent in
place,
Stl.ldent$ might
investlgate changM
wh$n the fold 1$
ITlO'led from
lengthwlsft to
widttlwlsft.
1fJ_~
From thl!l model
making eetlvlty.
$tudenls lIlhould ha\ffl
a$~thattNi
statlmlent lllll'lot
always l:rIJe, Slnoo tNi
areu of tNi trianguar
endlIl of the tal'lt
prllIlmlil ~not
In~lltMf.
~$tWentsto
qlJutkm~
~t'I($of~
~l1tements
considering ~
when
lIlweroont
Curriculum
C:l E:xpt'Cmtklu~
ApplieatitlniMarldng
Swme:A~ss
students' ability
to
calculatc the area and
volume of tOllngular
!'loam"
15
-l
!
i'"
i
s.
<
~
0"'"
I
i
c
::-f
iii
a.
(l>
(;)
~
:c.;:0
:0
t
I
I
I
+
t
I
I
I
+ ..
.,
til
3
...--til'"U
0)
C
-...
CD
::s
II
.~
_c.
"'
U)
.,"'
0
..
Unit 10: 08r10: Surface Area and Volume of Rectanlular Prisms
,"
.
•
'..
11th burniM
Grid• .,
MI"'.
!isl'"
dnv,.stigate the relatiot'l!hip between surface area and volume ofrecmnplar
• BLM lO.tO.!
prisms.
•
.....
•
AsH&llitnfHlt
•
Minds On."
Invle$tii~ ~lar Prisms to check:
re$1~~·Mdinvl~fitil~te additional
(Day () H.ome Activity)
•
Action!
student
elk! -+ 111Y,lIadsm
Students might
benefit frnm haIJlng
Pose the question:
have the same vmume.
have the Sl'!me surface
area?
BLM HUO.I:
.......i"....."
ProvlI:les a dyrnImic
I'I'lOdel of the paper
adMty,
Interlocking cubes to
help them Wiudi:e
the various $~
and" of bOxe:.s
with the same
is the surface area also the same?
of rectangular prism has th.e
area for a
volume?
moraeloo~
Individual :::t Ylrmen R!P9d
Stodents mdividually prepare a written
pritm. the
SUl'l'ac&
I.me._m_
"lit
to
of surface area
Communh:atinglPn\selltationlRatiug Scale: Assess students'
communicate in
and
thcir
~rtM
Dl prillm becol'l'lH to
volume as 11 result
has,
•
-+
Consolidate Whole.Cla!s
Student Pre!entatioD!
Debrief
Students
their findingl' and apply the mathematics learned in the
investiigat:ioo to answer this qUl~tion:
U"",in, A,u, curl
"(:U~~-tsrl."
Home ActMtx 2" Fuohe" Clas&roomConsoUdatloQ
Complete the practice questions,
TIPS4RM: Grade 1: Unit 10 - Volume of Right Prisms
PrcwIde students
appropriate
pradice qt.I&stiort$,
17
10.10.1: Wrapping Packages
Three different rectangular prism-shaped boxes each have a volume of 8 cubic units.
Does each box require the same amount of paper to wrap? Let's investigate!
2
1
1
2
2x2x2
2
2x4x1
1
1x8x1
1. a) Verify that each rectangular prism illustrated above has a volume of 8 cubic units.
b) Draw the net for each rectangular prism box.
c) Determine the amount of paper required by calculating the surface area.
(Ignore the overlapping pieces of paper you would need.)
d) Describe your findings.
2. a) How many different rectangular prism boxes can be designed to have a volume of 24
cubic units?
b) Draw several of the boxes, labelling the dimensions.
c) How much paper is required to wrap each box?
d) Describe your findings.
3. Investigate wrapping rectangular prism boxes with a volume of 36 cubic units.
Determine the dimensions of the rectangUlar prism with the greatest surface area.
4. Write a report of your findings. Include the following information, justifying your statements.
• Describe how surface area and volume are related, when the volume remains the same.
•
Describe the shape of a rectangUlar prism box that uses the most paper for a given
volume.
•
Describe the shape of a rectangUlar prism box the uses the least paper for a given
volume.
TIPS4RM: Gmde 1: Unit 10 - Volume of Right Prit>ma
18
5.1
Wrapping Gifts
(Grade 7)
Three different rectangular prism-shaped boxes each have a volume of 8 cubic units.
Does each box require the same amount of paper to wrap? let's investigate!
2
1
1
2
2x2x2
2
1
2x4xl
lx8xl
a
1. a) Verify that each rectangular prism iIIustra.ted above has a volume of cubic units.
b) Draw the net for each rectangular prism box,
c) Determine the amount of paper required by calculating the surface area.
(Ignore the overlapping pieces of paper you would need.)
d) Describe your findings.
r
2. a) How many different rectangular prism boxes can be designed to have a volume of 24
cubic units?
.
i
'83 i
l
b) Draw several of the boxes, labelling the dimensions.
1.-.
Ic) How much paper is required to wrap each box?
(.. .)
1d) Describe your findings.
".,.,. L f-~.
:t. ;(
r
y
I
'tl
3
y:. \
3. Investigate wrapping rectangular prism boxes with a volume of 36 cubic units. _.
Determine the dimensions of the rectangular prism with the greatest surface area.
3 ""' I-f'f,. J>
4. Write a report of your findings. Include the following information, justifying your statements.
• Describe how surface area and volume are related, when the volume remains the same.
•
What shape of rectangular prism box uses the most paper?
•
What shape of rectangular prism box uses the least paper?
TIPS:. $ec1l0tl :3 - Combined Grades 7 and 8
@ QUEletl's
PrlntElf for Ontario. 2004·
p$~\';
~
....
€t
l
J. ~
f
S-
I
~
~
I§
~
.,.,
.
.