Surface Area, Volume Surface Area, Volume and Density of Solidsand Density of Solids

Catherine P. LeonidaCatherine P. LeonidaEE3 3 Teacher Summer ProgramTeacher Summer Program

Texas A&M UniversityTexas A&M University20052005

Faculty: Dr. Helen (Hong) Liang Faculty: Dr. Helen (Hong) Liang Dr. Sudeep Ingole Dr. Sudeep Ingole

ObjectivesObjectives

To make polymers using non-toxic household To make polymers using non-toxic household materials.materials.To form solid figures (geometric shapes) out of To form solid figures (geometric shapes) out of these polymers.these polymers.To calculate the surface area, volume and To calculate the surface area, volume and density of solids. density of solids. To research on the characteristics and To research on the characteristics and geometric structures of some polymers. geometric structures of some polymers. To research on the practical applications of To research on the practical applications of polymers. polymers.

Texas Essential Knowledge and SkillsTexas Essential Knowledge and Skills

§111.34. Geometry§111.34. Geometry(a4) Students show the relationship (a4) Students show the relationship

between geometry, other mathematics, and other between geometry, other mathematics, and other disciplines. disciplines.

(a5) Students use a variety of (a5) Students use a variety of representations to solve meaningful problems.representations to solve meaningful problems.

(e1) Students extend measurement (e1) Students extend measurement concepts to find area, perimeter, and volume in concepts to find area, perimeter, and volume in problem situations. problem situations.

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

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

Proposed Schedule of ActivitiesProposed Schedule of Activities

Discussion on different solidsDiscussion on different solidsMaking polymers and shaping them into different Making polymers and shaping them into different solidssolidsCalculations of surface area, volume and density Calculations of surface area, volume and density of different solidsof different solidsDiscussion on polymers, its characteristics and Discussion on polymers, its characteristics and properties, including its geometric structuresproperties, including its geometric structuresPractical Applications of PolymersPractical Applications of PolymersPresentation on how the activity relates to other Presentation on how the activity relates to other fields of specializationfields of specialization

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

Sphere

Cube

Pyramid

Rectangular Prism

Cone

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

Other solidsOther solids

Tetragonal

Triangular Prism

Pentagonal Prism

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

Lesson 2: Making Plastics Lesson 2: Making Plastics (also known as Polymers)(also known as Polymers)

A. Divide the class into groups depending on A. Divide the class into groups depending on how many solids you would like them to how many solids you would like them to study (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 solid pyramid). Assign each group a solid figure to form.figure to form.

B. Prepare the materials ahead of B. Prepare the materials ahead of time.time.

You will need: You will need: Elmer’s glueElmer’s glue Tide Powdered laundry detergent (or Tide Powdered laundry detergent (or

Borax, if available)Borax, if available) Powdered StarchPowdered Starch Paper towelsPaper towels Plastic spoonsPlastic spoons WaterWater Small plastic cupsSmall plastic cups Straws or spoons for stirringStraws or spoons for stirring Different Food coloring (optional) – to vary Different Food coloring (optional) – to vary

the color of each solidthe color of each solid Vernier Caliper (when necessary)Vernier Caliper (when necessary) Platform balancePlatform balance

    Mess FactorMess Factor

Materials are not Materials are not toxic but not edible toxic but not edible either.either.Glue and Borax Glue and Borax can be washed off can be washed off with water.with water.Be careful with the Be careful with the use of food use of food coloring.coloring.

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

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

1.1. Mix 1 Mix 1 teaspoon of teaspoon of Elmer's glue, 1 Elmer's glue, 1 teaspoon of teaspoon of starch and 1 starch and 1 teaspoon of teaspoon of water in a small water in a small cup and stir.cup and stir.

2.2. In a separate In a separate cup, mix 1 cup, mix 1 teaspoon of Tide teaspoon of Tide powdered powdered laundry laundry detergent (or detergent (or Borax) with 2 Borax) with 2 teaspoons of teaspoons of water and stir.water and stir.

3.3. Combine the 2 Combine the 2 mixtures mixtures together in one together in one cup while stirring cup while stirring constantly until a constantly until a white glob forms. white glob forms.

4.4. Take the glob Take the glob out of the cup out of the cup and pat dry in and pat dry in between paper between paper towels. Pick up towels. Pick up the glob and see the glob and see what it feels like. what it feels like. 

*This procedure was adapted from the website: http://www.pslc.ws/macrog/kidsmac/property.htmGraphics courtesy of the same website

Formulas for Finding the Surface Formulas for Finding the Surface Area and Volume of SolidsArea and Volume of Solids

Surface Area of SolidsSurface Area of Solids

Cube S = 6sCube S = 6s

Cylinder (lateral) S = 2Cylinder (lateral) S = 2rh rh

Cylinder (total) S = 2Cylinder (total) S = 2rh + 2rh + 2rr22

Cone (lateral) S = Cone (lateral) S = rrll

Cone (total) S = Cone (total) S = rrll + + rr22

Sphere S = 4Sphere S = 4rr22

Volume of SolidsVolume of Solids

Prism or Cylinder V = BhPrism or Cylinder V = BhPyramid or Cone V = 1/3 BhPyramid or Cone V = 1/3 BhSphere V = 4/3 Sphere V = 4/3 rr33

Where Where 3.14 or 22/7 3.14 or 22/7 B = area of the baseB = area of the base

Classroom Activity: Classroom Activity: Data CollectionData Collection

Place the solids on different tables Place the solids on different tables or desks and have each group ‘visit’ or desks and have each group ‘visit’ each table/desk and measure the each table/desk and measure the dimensions of the figures. dimensions of the figures.

Instruct the students on which Instruct the students on which system of measurement to use, system of measurement to use, Metric or English.Metric or English.

CalculationsCalculations

Make a sketch of each solid and Make a sketch of each solid and label its parts. label its parts.

Show the formula used in finding the Show the formula used in finding the surface area and volume and the surface area and volume and the accompanying work with the accompanying work with the appropriate units. appropriate units.

Use the rules on significant figures. Use the rules on significant figures.

Lesson 3: Physical Characteristics Lesson 3: Physical Characteristics of Some Polymersof Some Polymers

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

i. polymersi. polymers

ii. substances (active ii. substances (active ingredients) present in the ingredients) present in the polymer they made.polymer they made.

iii. characteristics and examples iii. characteristics and examples of the geometric structures of of the geometric structures of some polymers.some polymers.

Chemistry: Active Substances in Polymers

Teacher’s notesTeacher’s notes:: What are polymers??? What are polymers???Polymers are naturally occurring Polymers are naturally occurring or synthetically made materials or synthetically made materials composed of molecules of simple composed of molecules of simple monomers linked together. Their monomers linked together. Their wide range of properties make wide range of properties make them very useful to people. They them very useful to people. They are normally present in materials are normally present in materials used in food production because used in food production because they have very little additives. they have very little additives.

Two major groups of polymer are Two major groups of polymer are plastics and elastomers. Plastics plastics and elastomers. Plastics are widely used due to their ability are widely used due to their ability to be molded. Elastomers (or to be molded. Elastomers (or rubbers) are popular because of rubbers) are popular because of their ability to be bent upon the their ability to be bent upon the exertion of a force and return to exertion of a force and return to their original shape upon the their original shape upon the release of the same force. release of the same force.

Polymers are composed of chains Polymers are composed of chains of covalent-bonded atoms like the of covalent-bonded atoms like the ones shown below. The chains are ones shown below. The chains are held together by secondary bonds. held together by secondary bonds.

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

Teacher’s notes:Teacher’s notes: Substances (active Substances (active ingredients) Present in Polymeringredients) Present in Polymer

When Elmer's glue is combined with water, a substance that is When Elmer's glue is combined with water, a substance that is known as a polymer known as a polymer (polyvinyl acetate)(polyvinyl acetate) is formed. The borax is formed. The borax solution solution (sodium tetraborate)(sodium tetraborate) is a 'cross-linking' substance that is a 'cross-linking' substance that binds 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 to Adding more Borax or Tide detergent is like adding more chains to the 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 this Knowing just how much Borax solution to add is the trick to this experiment. You know if you put too much Borax solution if the experiment. You know if you put too much Borax solution if the polymer is very wet and slippery (because of the soap solution- the polymer is very wet and slippery (because of the soap solution- the cross linking part!). Similarly, if you put too little, you end up with one cross linking part!). Similarly, if you put too little, you end up with one that is too sticky (you have more Elmer’s glue solution – the polymer that is too sticky (you have more Elmer’s glue solution – the polymer part). part).

http://sciencespot.net/Pages/classchem.html#Anchor-polyhttp://sciencespot.net/Pages/classchem.html#Anchor-poly

Models of some polymers.Models of some polymers.

Chemical Structures of Some Chemical Structures of Some PolymersPolymers

Atoms of polymers ‘wanting’ to be manipulated to Atoms of polymers ‘wanting’ to be manipulated to enhance their properties and capabilities…enhance their properties and capabilities…

Geometric shapes are also apparent in Nature. Below are snowflakes showing

different shapes.

Geometric shapes in Geometric shapes in nanotechnolgynanotechnolgy

Buckminster Fullerene or ‘Bucky Ball’ – 60 atoms forming pentagons and hexagons Two Bucky balls joined together

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.com

http://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/polymers1.htmhttp://spider.chemphys.lu.se/~wichard/polymers1.htm

Pictures of previous polymer models were taken from the above websites

Some Physical Properties of Some Physical Properties of PolymersPolymers

Property that enables them to be pulled

--

tensile strength

Property that enables 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

sharp blows/impacts--

impact strength

IPC: Physical properties of Matter

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

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/WofMatE/polymers.htm

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

Why study the different properties of Why study the different properties of materials including their geometric materials 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 to everything from the strength and electrical conductivity to optical, magnetic and thermal properties has the potential to be optical, magnetic and thermal properties has the potential to be modified.modified.

Application in the field of bio-nanotechnology: There is a Application in the field of bio-nanotechnology: There is a growing interest in the understanding of the response of growing interest in the understanding of the response of biological systems to foreign materials. More and more biological systems to foreign materials. More and more researches are undertaken in this field. The biocompatibility of researches are undertaken in this field. The biocompatibility of materials is determined by the material’s ability to successfully materials is determined by the material’s ability to successfully fulfill the function it was designed for when placed in a fulfill the function it was designed for when placed in a biological system. Strength, thickness, roughness, biological system. Strength, thickness, roughness, composition, heterogeneity, electronic properties, structure composition, 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’

How does our activity How does our activity connect to other connect to other

areas of areas of specialization?specialization?

Polymers and ceramics are used Polymers and ceramics are used as coatings in implants and artificial as coatings in implants and artificial

jointsjoints

Graphics courtesy of TEES

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.

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

Samples of boron particles subjected to Samples of boron particles subjected to ultrasonic energy viewed under a ultrasonic 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 !!!

Lesson 4: Density of MaterialsLesson 4: Density of Materials

Ask each group to weigh the solid assigned to them and have them write Ask each group to weigh the solid assigned to them and have them write the result on the board to make available to the entire class the mass of the the result on the board to make available to the entire class the mass of the different solids. different solids. Once they all have the mass and volume, ask each group to calculate the Once they all have the mass and volume, ask each group to calculate the density 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 jar because of their shape.

IPC or Algebra: Direct or Inverse Variation

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 different Ask them to create rectangular prisms with different sizes using the procedures described above. sizes using the procedures described above. Instruct the class to calculate the surface area and Instruct the class to calculate the surface area and volume 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 of Investigate how the ratio changes as the dimensions of the structure shrinks. See if there is a mathematical the structure shrinks. See if there is a mathematical equation 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 the Research on the implications of the activity in the nanoworld. nanoworld.

Algebra: Creating Mathematical Models or Functions

Lesson 6: Creating a Lesson 6: Creating a 3-D Model of Bucky ball 3-D Model of Bucky ball

Materials:Materials:

- pipe cleaners- pipe cleaners

- 60 styrofoam balls- 60 styrofoam balls

Procedure:Procedure:

Have students form pentagons and hexagons Have students form pentagons and hexagons using pipe cleaners and 60 styrofoam balls. using pipe cleaners and 60 styrofoam balls. They will realize that they cannot completely ‘tile’ They will realize that they cannot completely ‘tile’ a surface with pure hexagons – they would need a surface with pure hexagons – they would need pentagons to create the Bucky ball. pentagons to create the Bucky ball.

Geometry: Creating a 3-D model using geometrical shapes

AcknowledgmentsAcknowledgments

EE33 Organizing Committee Organizing Committee

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

Dr. Helen Liang & her Dr. Helen Liang & her Graduate Students Graduate Students

Dr. Sudeep Ingole Dr. Sudeep Ingole

Dr. Saibal MitraDr. Saibal Mitra

Staff of MiC LaboratoryStaff of MiC Laboratory

Orlando PatricioOrlando Patricio