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Surface Area, VolumeSurface Area, Volumeand Density of Solidsand Density of Solids

Catherine P. LeonidaCatherine P. Leonida

EE33 Teacher Summer ProgramTeacher Summer Program

Texas A&M UniversityTexas A&M University

20052005

Faculty: Dr. Helen (Hong) LiangFaculty: Dr. Helen (Hong) Liang

Dr. Sudeep IngoleDr. Sudeep Ingole

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ObjectivesObjectives

To make polymers using nonTo make polymers using non--toxic householdtoxic householdmaterials.materials.

To form solid figures (geometric shapes) out ofTo form solid figures (geometric shapes) out of

these polymers.these polymers.To calculate the surface area, volume andTo calculate the surface area, volume anddensity of solids.density of solids.

To research on the characteristics andTo research on the characteristics and

geometric structures of some polymers.geometric structures of some polymers.To research on the practical applications ofTo research on the practical applications ofpolymers.polymers.

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Texas Essential Knowledge and SkillsTexas Essential Knowledge and Skills

111.34. Geometry111.34. Geometry

(a(a44)) StudentsStudents showshow thethe relationshiprelationshipbetweenbetween geometry,geometry, otherother mathematics,mathematics, andandotherother disciplinesdisciplines..

(a(a55)) StudentsStudents useuse aa varietyvariety of ofrepresentationsrepresentations toto solvesolve meaningfulmeaningful problemsproblems..

(e1) Students extend measurement(e1) Students extend measurement

concepts to find area, perimeter, and volume inconcepts to find area, perimeter, and volume inproblem situations.problem situations.

(e4) Students describe the effect on(e4) Students describe the effect onperimeter, area, and volume when length,perimeter, area, and volume when length,width, or height of a threewidth, or height of a three--dimensional solid isdimensional solid is

changed.changed.http://www.utdanacenter.org/http://www.utdanacenter.org/

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Proposed Schedule of ActivitiesProposed Schedule of Activities

Discussion on different solidsDiscussion on different solids

Making polymers and shaping them into differentMaking polymers and shaping them into differentsolidssolids

Calculations of surface area, volume and densityCalculations of surface area, volume and densityof different solidsof different solids

Discussion on polymers, its characteristics andDiscussion on polymers, its characteristics andproperties, including its geometric structuresproperties, including its geometric structures

Practical Applications of PolymersPractical Applications of PolymersPresentation on how the activity relates to otherPresentation on how the activity relates to otherfields of specializationfields of specialization

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Lesson 1: Discussion on Different SolidsLesson 1: Discussion on Different Solids

Sphere

Cube

Pyramid

Rectangular Prism

Cone

Graphics Courtesy ofhttp://www.mathleague.com/help/geometry/3space.htm#surfacearea

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Other solidsOther solids

Tetragonal

Triangular Prism

Pentagonal Prism

Cylinderhttp://www.mathleague.com/help/geometry/3space.htm#surfacearea

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Lesson 2: Making PlasticsLesson 2: Making Plastics

(also known as Polymers)(also known as Polymers)

A. Divide the class into groups depending onA. Divide the class into groups depending on

how many solids you would like them tohow many solids you would like them tostudy (e.g., cube, rectangular prism,study (e.g., cube, rectangular prism,

triangular prism, pentagonal prism,triangular prism, pentagonal prism,

hexagonal prism, cylinder, sphere,hexagonal prism, cylinder, sphere,

pyramid). Assign each group a solidpyramid). Assign each group a solid

figure to form.figure to form.

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B. Prepare the materials ahead ofB. Prepare the materials ahead of

time.time.You will need:You will need:

Elmers glueElmers glue

Tide Powdered laundry detergent (orTide Powdered laundry detergent (orBorax, if available)Borax, if available)

Powdered StarchPowdered Starch

Paper towelsPaper towels

Plastic spoonsPlastic spoons

WaterWater

Small plastic cupsSmall plastic cupsStraws or spoons for stirringStraws or spoons for stirring

Different Food coloring (optional)Different Food coloring (optional) to varyto varythe color of each solidthe color of each solid

Vernier Caliper (when necessary)Vernier Caliper (when necessary)

Platform balancePlatform balance

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Mess FactorMess Factor

Materials are notMaterials are nottoxic but not edibletoxic but not edibleeither.either.

Glue and BoraxGlue and Boraxcan be washed offcan be washed offwith water.with water.

Be careful with theBe careful with theuse of fooduse of foodcoloring.coloring.

Graphics courtesy of

http://www.pslc.ws/macrog/kidsmac/property.htm

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C. Procedure on making the polymer*C. Procedure on making the polymer*

1.1. Mix 1Mix 1

teaspoon ofteaspoon of

Elmer's glue, 1Elmer's glue, 1teaspoon ofteaspoon of

starch and 1starch and 1

teaspoon ofteaspoon ofwater in a smallwater in a small

cup and stir.cup and stir.

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2.2. In a separateIn a separate

cup, mix 1cup, mix 1

teaspoon of Tideteaspoon of Tide

powderedpowderedlaundrylaundry

detergent (ordetergent (or

Borax) with 2Borax) with 2teaspoons ofteaspoons of

water and stir.water and stir.

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3.3. Combine the 2Combine the 2

mixturesmixtures

together in onetogether in onecup while stirringcup while stirring

constantly until aconstantly until a

white glob forms.white glob forms.

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4.4. Take the globTake the glob

out of the cupout of the cup

and pat dry inand pat dry inbetween paperbetween paper

towels. Pick uptowels. Pick up

the glob and seethe glob and seewhat it feels like.what it feels like.

*This procedure was adapted from the website:

http://www.pslc.ws/macrog/kidsmac/property.htm

Graphics courtesy of the same website

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Formulas for Finding the SurfaceFormulas for Finding the Surface

Area and Volume of SolidsArea and Volume of SolidsSurface Area of SolidsSurface Area of Solids

Cube S = 6sCube S = 6s

Cylinder (lateral) S = 2Cylinder (lateral) S = 2TTrhrh

Cylinder (total) S = 2Cylinder (total) S = 2TTrh + 2rh + 2TTrr22

Cone (lateral) S =Cone (lateral) S = TTrrll

Cone (total) S =Cone (total) S = TTrrll++ TTrr22

Sphere S = 4Sphere S = 4TTrr22

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Volume of SolidsVolume of Solids

Prism or Cylinder V = BhPrism or Cylinder V = Bh

Pyramid or Cone V = 1/3B

hPyramid or Cone V = 1/3B

hSphere V = 4/3Sphere V = 4/3 TTrr33

WhereWhere TT }} 3.14 or 22/73.14 or 22/7B = area of the baseB = area of the base

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Classroom Activity:Classroom Activity:

Data CollectionData Collection

Place the solids on different tablesPlace the solids on different tables

or desks and have each group visitor desks and have each group visiteach table/desk and measure theeach table/desk and measure the

dimensions of the figures.dimensions of the figures.

Instruct the students on whichInstruct the students on whichsystem of measurement to use,system of measurement to use,

Metric or English.Metric or English.

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CalculationsCalculations

Make a sketch of each solid andMake a sketch of each solid and

label its parts.label its parts.

Show the formula used in finding theShow the formula used in finding thesurface area and volume and thesurface area and volume and the

accompanying work with theaccompanying work with the

appropriate units.appropriate units.Use the rules on significant figures.Use the rules on significant figures.

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Lesson 3: Physical CharacteristicsLesson 3: Physical Characteristics

of Some Polymersof Some Polymers

Have the class research on:Have the class research on:

i. polymersi. polymers

ii. substances (activeii. substances (activeingredients) present in theingredients) present in the

polymer they made.polymer they made.

iii. characteristics and examplesiii. characteristics and examplesof the geometric structures ofof the geometric structures of

some polymers.some polymers.

Chemistry: Active Substances in Polymers

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Teachers notesTeachers notes:: What are polymers???What are polymers???

Polymers are naturally occurringPolymers are naturally occurringor synthetically made materialsor synthetically made materialscomposed of molecules of simplecomposed of molecules of simplemonomers linked together. Theirmonomers linked together. Theirwide range of properties makewide range of properties makethem very useful to people. Theythem very useful to people. They

are normally present in materialsare normally present in materialsused in food production becauseused in food production becausethey have very little additives.they have very little additives.

Two major groups of polymer areTwo major groups of polymer areplastics and elastomers. Plasticsplastics and elastomers. Plasticsare widely used due to their abilityare widely used due to their ability

to be molded. Elastomers (orto be molded. Elastomers (orrubbers) are popular because ofrubbers) are popular because oftheir ability to be bent upon thetheir ability to be bent upon theexertion of a force and return toexertion of a force and return totheir original shape upon thetheir original shape upon therelease of the same force.release of the same force.

Polymers are composed of chainsPolymers are composed of chains

of covalentof covalent--bonded atoms like thebonded atoms like the

ones shown below. The chainsones shown below. The chains

are held together by secondaryare held together by secondary

bonds.bonds.

http://www.engr.sjsu.edu/WofMatE/polymers.htm

http://www.cem.msu.edu/~bakerg/science_olympiad/Polymer_Detective_Presentation.pdf#search='polymers%20for%20high%20school

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Teachers notes:Teachers notes: Substances (activeSubstances (active

ingredients) Present in Polymeringredients) Present in PolymerWhen Elmer's glue is combined with water, a substance that isWhen Elmer's glue is combined with water, a substance that isknown as a polymerknown as a polymer(polyvinyl acetate)(polyvinyl acetate) is formed. The boraxis formed. The boraxsolutionsolution (sodium tetraborate)(sodium tetraborate) is a 'crossis a 'cross--linking' substance thatlinking' substance thatbinds the polymer chains together making the glue solution thicker.binds the polymer chains together making the glue solution thicker.Adding more Borax or Tide detergent is like adding more chains toAdding more Borax or Tide detergent is like adding more chains tothe polymer making it harder to move the polymer around.the polymer making it harder to move the polymer around.

Knowing just how much Borax solution to add is the trick to thisKnowing just how much Borax solution to add is the trick to thisexperiment. You know if you put too much Borax solution if theexperiment. You know if you put too much Borax solution if the

polymer is very wet and slippery (because of the soap solutionpolymer is very wet and slippery (because of the soap solution-- thethecross linking part!). Similarly, if you put too little, you end up with onecross linking part!). Similarly, if you put too little, you end up with onethat is too sticky (you have more Elmers glue solutionthat is too sticky (you have more Elmers glue solution the polymerthe polymerpart).part).

http://sciencespot.net/Pages/classchem.html#Anchorhttp://sciencespot.net/Pages/classchem.html#Anchor--polypoly

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Models of some polymers.Models of some polymers.

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Chemical Structures of SomeChemical Structures of Some

PolymersPolymers

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Atoms of polymers wanting to be manipulated toAtoms of polymers wanting to be manipulated to

enhance their properties and capabilitiesenhance their properties and capabilities

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Geometric shapes are also apparent in

Nature. Below are snowflakes showing

different shapes.

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Geometric shapes inGeometric shapes in

nanotechnolgynanotechnolgy

Buckminster Fullerene or

Bucky Ball 60 atoms

forming pentagons and

hexagons Two Bucky balls joined together

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Websites on PolymersWebsites on Polymers

http://www.qemi.com/html/polymers.htmhttp://www.qemi.com/html/polymers.htm

http://www.ims.uconn.edu/~avd/PhysicsGroup/polymers.htmlhttp://www.ims.uconn.edu/~avd/PhysicsGroup/polymers.html

http://www.trianglechemical.com/polymers.htmlhttp://www.trianglechemical.com/polymers.html

www.clas.uconn.eduwww.clas.uconn.edu

http://www.bakerhughes.comhttp://www.bakerhughes.comhttp://www.polymer.cz/enghttp://www.polymer.cz/eng

http://www.greenspirit.org.uk/resources/LifeChemistry.htmhttp://www.greenspirit.org.uk/resources/LifeChemistry.htm

http://www.dcci.unipi.it/~bea/eupoc03http://www.dcci.unipi.it/~bea/eupoc03http://spider.chemphys.lu.se/~wichard/http://spider.chemphys.lu.se/~wichard/

polymers1.htmpolymers1.htm

Pictures of previous polymer models were taken from the above websites

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Some Physical Properties ofSome Physical Properties of

PolymersPolymers

Property that

enables them to

be pulled --

tensile

strength

Property thatenables them to

be compressed --

compressional

strength

Property that

enables them to

bend --

flexural

strength

Property that

enables them to

be twisted --

torsional

strength

Property that allows

them to tolerate

sharpblows/impacts--

impact

strength

IPC: Physical properties of Matter

Graphics courtesy ofhttp://www.pslc.ws/macrog/kidsmac/property.htm

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Practical Applications of PolymersPractical Applications of Polymers

www.bakerhughes.com/

www.st-and.ac.uk

www.degussa-hpp.com

www.wehmer.com

www.bakerhughes.com

Computer printer Plastic tubes Eye glasses

Plastic Retainers Vending machine Cellphone covers

pubs.acs.org

Roller Skates

Two-way radios

http://www.engr.sjsu.edu/WofMat

E/polymers.htm

http://www.engr.sjsu.edu/WofMatE/polymers.htm

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Why study the different properties ofWhy study the different properties of

materials including their geometricmaterials including their geometric

structures?structures?If a material is manipulated on its atomic or molecular level,If a material is manipulated on its atomic or molecular level,

everything from the strength and electrical conductivity toeverything from the strength and electrical conductivity to

optical, magnetic and thermal properties has the potential tobeoptical, magnetic and thermal properties has the potential tobe

modified.modified.

Application in the field ofbioApplication in the field ofbio--nanotechnology: There is ananotechnology: There is a

growing interest in the understanding of the response ofgrowing interest in the understanding of the response of

biological systems to foreign materials. More and morebiological systems to foreign materials. More and more

researches are undertaken in this field. The biocompatibility ofresearches are undertaken in this field. The biocompatibility of

materials is determined by the materials ability to successfullymaterials is determined by the materials ability to successfullyfulfill the function it was designed for when placed in afulfill the function it was designed for when placed in a

biological system. Strength, thickness, roughness,biological system. Strength, thickness, roughness,

composition, heterogeneity, electronic properties, structurecomposition, heterogeneity, electronic properties, structure

and wettability, all of which play a role in cell interaction.and wettability, all of which play a role in cell interaction.

Seema H. Bajaria and Anuj Bellare. Deformation, Morphology, and Wear Behavior of Polyethylene Used in Orthopedic Implants

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How does our activityHow does our activityconnect to otherconnect to other

areas ofareas of

specialization?specialization?

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Polymers and ceramics are usedPolymers and ceramics are used

as coatings in implants and artificialas coatings in implants and artificial

jointsjoints

Graphics courtesy of TEES

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Si substrate

Interconnect

Extension of artifacial

joints lifespan.

Processes to make small chips.

New

nanomanufacturing

processes for

nanocrystals.Surface and

interface in

synergetic

systems.

E3-Research Projects

Self-repairing railroad tracks.

Novel

sensors.

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Sonomaterials new process to make nanomaterialsApproach: ultrasound, microscopes (opt., e-, etc.)

Biomaterials investigate failure mechanisms of chicken

jointsApproach: test friction and wear in biofluids, tribometer

E3-Research Projects

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Samples of boron particles subjected toSamples of boron particles subjected to

ultrasonic energy viewed under aultrasonic energy viewed under a

Scanning Electron Microscope (SEM)Scanning Electron Microscope (SEM)

Notice the different structures whose

shapes are similar to the ones studied in

a geometry class !!!

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Lesson 4: Density of MaterialsLesson 4: Density of Materials

Ask each group to weigh the solid assigned to them and have them writeAsk each group to weigh the solid assigned to them and have them writethe result on the board to make available to the entire class the mass of thethe result on the board to make available to the entire class the mass of thedifferent solids.different solids.

Once they all have the mass and volume, ask each group to calculate theOnce they all have the mass and volume, ask each group to calculate thedensity of all solids, with appropriate units.density of all solids, with appropriate units.

FYI: Recent discovery shows that M&Ms are highest packed

in a jarbecause of their shape.

IPC or Algebra: Direct orInverse Variation

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Lesson 5: Varying DimensionsLesson 5: Varying Dimensions

Have the class stick to one solid, say rectangular prism.Have the class stick to one solid, say rectangular prism.Ask them to create rectangular prisms with differentAsk them to create rectangular prisms with differentsizes using the procedures described above.sizes using the procedures described above.

Instruct the class to calculate the surface area andInstruct the class to calculate the surface area andvolume of the solids created and compute for their ratios.volume of the solids created and compute for their ratios.

Investigate how the ratio changes as the dimensions ofInvestigate how the ratio changes as the dimensions ofthe structure shrinks. See if there is a mathematicalthe structure shrinks. See if there is a mathematicalequation that would model the situation (linear,equation that would model the situation (linear,exponential, power function, etc.)exponential, power function, etc.)

Research on the implications of the activity in theResearch on the implications of the activity in thenanoworld.nanoworld.

Algebra: Creating Mathematical Models or Functions

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Lesson 6: Creating aLesson 6: Creating a

33--D Model ofBucky ballD Model ofBucky ball

Materials:Materials:

-- pipe cleanerspipe cleaners-- 60 styrofoam balls60 styrofoam balls

Procedure:Procedure:

HaveHave studentsstudents formform pentagonspentagons andand hexagonshexagons

usingusing pipepipe cleanerscleaners andand 6060 styrofoamstyrofoam ballsballs..

TheyThey willwill realizerealize thatthat theythey cannotcannot completelycompletely tiletile

aa surfacesurface withwith purepure hexagonshexagons theythey wouldwould needneed

pentagonspentagons toto createcreate thethe BuckyBucky ballball..

Geometry: Creating a 3-D model using geometrical shapes

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AcknowledgmentsAcknowledgments

EE33 Organizing CommitteeOrganizing Committee

(led by Jan Rinehart)(led by Jan Rinehart)

Dr. Helen Liang & herDr. Helen Liang & her

Graduate StudentsGraduate Students

Dr. Sudeep IngoleDr. Sudeep Ingole

Dr. Saibal MitraDr. Saibal Mitra

Staff of MiC LaboratoryStaff of MiC Laboratory

Orlando PatricioOrlando Patricio