Surface Area, Volume and Density of Solids

1. Surface Area, Volume and Density of Solids Catherine P. Leonida E3 Teacher Summer Program Texas A&M University 2005 Faculty: Dr. Helen (Hong) Liang Dr. Sudeep Ingole

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

3. Texas Essential Knowledge and Skills §111.34. Geometry (a4) Students show the relationship between geometry, other mathematics, and other disciplines. (a5) Students use a variety of representations to solve meaningful problems. (e1) Students extend measurement concepts to find area, perimeter, and volume in problem situations. (e4) Students describe the effect on perimeter, area, and volume when length, width, or height of a three-dimensional solid is changed. http://www.utdanacenter.org/

4. Proposed Schedule of Activities • Discussion on different solids • Making polymers and shaping them into different solids • Calculations of surface area, volume and density of different solids • Discussion on polymers, its characteristics and properties, including its geometric structures • Practical Applications of Polymers • Presentation on how the activity relates to other fields of specialization

5. Lesson 1: Discussion on Different Solids Rectangular Prism Cube Sphere Cone Pyramid Graphics Courtesy of http://www.mathleague.com/help/geometry/3space.htm#surfacearea

6. Other solids Pentagonal Prism Tetragonal Triangular Prism Cylinder http://www.mathleague.com/help/geometry/3space.htm#surfacearea

7. Lesson 2: Making Plastics (also known as Polymers) A. Divide the class into groups depending on how many solids you would like them to study (e.g., cube, rectangular prism, triangular prism, pentagonal prism, hexagonal prism, cylinder, sphere, pyramid). Assign each group a solid figure to form.

8. B. Prepare the materials ahead of time. You will need: Elmer’s glue Tide Powdered laundry detergent (or Borax, if available) Powdered Starch Paper towels Plastic spoons Water Small plastic cups Straws or spoons for stirring Different Food coloring (optional) – to vary the color of each solid Vernier Caliper (when necessary) Platform balance

9. Mess Factor • Materials are not toxic but not edible either. • Glue and Borax can be washed off with water. • Be careful with the use of food coloring. Graphics courtesy of http://www.pslc.ws/macrog/kidsmac/property.htm

10. C. Procedure on making the polymer* • 1. Mix 1 teaspoon of Elmer's glue, 1 teaspoon of starch and 1 teaspoon of water in a small cup and stir.

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

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

13. 4. Take the glob out of the cup and pat dry in between paper towels. Pick up the glob and see 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

14. Formulas for Finding the Surface Area and Volume of Solids Surface Area of Solids • Cube S = 6s • Cylinder (lateral) S = 2rh • Cylinder (total) S = 2rh + 2r2 • Cone (lateral) S = rl • Cone (total) S = rl + r2 • Sphere S = 4r2

15. Volume of Solids • Prism or Cylinder V = Bh • Pyramid or Cone V = 1/3 Bh • Sphere V = 4/3 r3 Where  3.14 or 22/7 B = area of the base

16. Classroom Activity: Data Collection • Place the solids on different tables or desks and have each group ‘visit’ each table/desk and measure the dimensions of the figures. • Instruct the students on which system of measurement to use, Metric or English.

17. Calculations • Make a sketch of each solid and label its parts. • Show the formula used in finding the surface area and volume and the accompanying work with the appropriate units. • Use the rules on significant figures.

18. Lesson 3: Physical Characteristics of Some Polymers Chemistry: Active Substances in Polymers Have the class research on: i. polymers ii. substances (active ingredients) present in the polymer they made. iii. characteristics and examples of the geometric structures of some polymers.

19. Polymers are naturally occurring or synthetically made materials composed of molecules of simple monomers linked together. Their wide range of properties make them very useful to people. They are normally present in materials used in food production because they have very little additives. Two major groups of polymer are plastics and elastomers. Plastics are widely used due to their ability to be molded. Elastomers (or rubbers) are popular because of their ability to be bent upon the exertion of a force and return to their original shape upon the release of the same force. Polymers are composed of chains of covalent-bonded atoms like the ones shown below. The chains are held together by secondary bonds. Teacher’s notes: What are polymers??? 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

20. Teacher’s notes: Substances (active ingredients) Present in Polymer When Elmer's glue is combined with water, a substance that is known as a polymer (polyvinyl acetate) is formed. The borax solution (sodium tetraborate) is a 'cross-linking' substance that binds the polymer chains together making the glue solution thicker. Adding more Borax or Tide detergent is like adding more chains to the polymer making it harder to move the polymer around. 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 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 that is too sticky (you have more Elmer’s glue solution – the polymer part). http://sciencespot.net/Pages/classchem.html#Anchor-poly

21. Models of some polymers.

22. Chemical Structures of Some Polymers

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

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

25. Geometric shapes in nanotechnolgy Buckminster Fullerene or ‘Bucky Ball’ – 60 atoms forming pentagons and hexagons Two Bucky balls joined together

26. Websites on Polymers • http://www.qemi.com/html/polymers.htm • http://www.ims.uconn.edu/~avd/PhysicsGroup/polymers.html • http://www.trianglechemical.com/polymers.html • www.clas.uconn.edu • http://www.bakerhughes.com • http://www.polymer.cz/eng • http://www.greenspirit.org.uk/resources/LifeChemistry.htm • http://www.dcci.unipi.it/~bea/eupoc03http://spider.chemphys.lu.se/~wichard/polymers1.htm Pictures of previous polymer models were taken from the above websites

27. Some Physical Properties of Polymers IPC: Physical properties of Matter Graphics courtesy of http://www.pslc.ws/macrog/kidsmac/property.htm

28. Practical Applications of Polymers Computer printer Plastic tubes Eye glasses Roller Skates www.bakerhughes.com/ www.degussa-hpp.com www.st-and.ac.uk http://www.engr.sjsu.edu/WofMatE/polymers.htm Plastic Retainers Vending machine Cellphone covers Two-way radios www.wehmer.com pubs.acs.org http://www.engr.sjsu.edu/WofMatE/polymers.htm www.bakerhughes.com

29. Why study the different properties of materials including their geometric structures? • If a material is manipulated on its atomic or molecular level, everything from the strength and electrical conductivity to optical, magnetic and thermal properties has the potential to be modified. • Application in the field of bio-nanotechnology: There is a growing interest in the understanding of the response of biological systems to foreign materials. More and more researches are undertaken in this field. The biocompatibility of materials is determined by the material’s ability to successfully fulfill the function it was designed for when placed in a biological system. Strength, thickness, roughness, composition, heterogeneity, electronic properties, structure 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’

30. How does our activity connect to other areas of specialization?

31. Polymers and ceramics are used as coatings in implants and artificial joints Graphics courtesy of TEES

32. Interconnect Si substrate E3-Research Projects Novel sensors. New nanomanufacturing processes for nanocrystals. Surface and interface in synergetic systems. Extension of artifacial joints’ lifespan. Processes to make small chips. Self-repairing railroad tracks.

33. E3-Research Projects Sonomaterials – new process to make nanomaterials Approach: ultrasound, microscopes (opt., e-, etc.) Biomaterials – investigate failure mechanisms of chicken joints Approach: test friction and wear in biofluids, tribometer

34. Samples of boron particles subjected to ultrasonic energy viewed under a Scanning Electron Microscope (SEM) Notice the different structures whose shapes are similar to the ones studied in a geometry class !!!

35. Lesson 4: Density of Materials IPC or Algebra: Direct or Inverse Variation • 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 different solids. • Once they all have the mass and volume, ask each group to calculate the density of all solids, with appropriate units. FYI: Recent discovery shows that M&Ms are highest packed in a jar because of their shape.

36. Lesson 5: Varying Dimensions Algebra: Creating Mathematical Models or Functions • Have the class stick to one solid, say rectangular prism. Ask them to create rectangular prisms with different sizes using the procedures described above. • Instruct the class to calculate the surface area and volume of the solids created and compute for their ratios. • Investigate how the ratio changes as the dimensions of the structure shrinks. See if there is a mathematical equation that would model the situation (linear, exponential, power function, etc.) • Research on the implications of the activity in the nanoworld.

37. Lesson 6: Creating a 3-D Model of Bucky ball • Materials: - pipe cleaners - 60 styrofoam balls • Procedure: Have students form pentagons and hexagons using pipe cleaners and 60 styrofoam balls. They will realize that they cannot completely ‘tile’ a surface with pure hexagons – they would need pentagons to create the Bucky ball. Geometry: Creating a 3-D model using geometrical shapes

38. Acknowledgments • E3 Organizing Committee (led by Jan Rinehart) • Dr. Helen Liang & her Graduate Students • Dr. Sudeep Ingole • Dr. Saibal Mitra • Staff of MiC Laboratory • Orlando Patricio