Surface Area, Volume and Density of Solids

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Surface Area, Volume and Density of Solids

• Catherine P. Leonida
• E3 Teacher Summer Program
• Texas AM University
• 2005
• Faculty Dr. Helen (Hong) Liang
• Dr. Sudeep Ingole

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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.

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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/
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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

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Lesson 1 Discussion on Different Solids


Rectangular Prism
Cube
Sphere
Cone
Pyramid
Graphics Courtesy of http//www.mathleague.com/hel
p/geometry/3space.htmsurfacearea
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Other solids
Pentagonal Prism
Tetragonal
Triangular Prism
Cylinder
http//www.mathleague.com/help/geometry/3space.htm
surfacearea
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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.

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B. Prepare the materials ahead of time.

• You will need
• Elmers 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

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  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/kid
smac/property.htm
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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.

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

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

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• 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 Gra
phics courtesy of the same website
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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

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• 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

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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.

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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.

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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.

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Teachers notes What are polymers???

• 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.

http//www.engr.sjsu.edu/WofMatE/polymers.htm http
//www.cem.msu.edu/bakerg/science_olympiad/Polyme
r_Detective_Presentation.pdfsearch'polymers20fo
r20high20school
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Teachers 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 Elmers glue solution the
  polymer part).

http//sciencespot.net/Pages/classchem.htmlAnchor
-poly
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Models of some polymers.
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Chemical Structures of Some Polymers
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Atoms of polymers wanting to be manipulated to
enhance 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 in nanotechnolgy
Buckminster Fullerene or Bucky Ball 60 atoms
forming pentagons and hexagons
Two Bucky balls joined together
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Websites on Polymers

• http//www.qemi.com/html/polymers.htm
• http//www.ims.uconn.edu/avd/PhysicsGroup/polymer
  s.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/LifeChemis
  try.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
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Some Physical Properties of Polymers
IPC Physical properties of Matter
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
Graphics courtesy of http//www.pslc.ws/macrog/kid
smac/property.htm
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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
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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 materials 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
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How does our activity connect to other areas of
specialization?
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Polymers and ceramics are used as coatings in
implants and artificial joints
Graphics courtesy of TEES
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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.
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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
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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
!!!
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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 MMs are
highest packed in a jar because of their shape.
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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.

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Lesson 6 Creating a 3-D Model of Bucky ball
Geometry Creating a 3-D model using geometrical
shapes

• 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.

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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