the fourth plinth
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The Fourth PlinthThe Fourth PlinthPolyhedral Life
Theme:The OlympicsTask:Design a sculpture linked to the Olympics using polyhedra.
Background:The fourth plinth in Trafalgar Square is an empty pedestal that has been empty since 1841.Over the past number of years there has been a changing exhibition of different sculptures on it, including Anthony Gormley's "The One and the Other". Over 100 days, members of the public stood on the plinth 24 hours a day.
Your structure needs to take the place of the
cowboy picture
What dimensions does it need to be?
Here are a selection of polyhedra you
may wish to consider in your planning
Cube
Hexagonal prism
Pentagonal prism
Triangular prism
Octagonal prism
Cuboid
Cylinder
Materials
When you make your model/sculpture, you can choose to construct it from a wide variety of materials. These may include the following:
• Carving of wood, stone, plaster and cement• Welding of metal (steel and copper) plates• Twisting and wrapping of wire• Modeling of forms in clay, wax and plaster• Casting of bronze, steel and plastic• Working in iron and copper• Blowing or moulding of glass
The following slide shows examples of statues made from different materials to give you an idea of the finish and aesthetic qualities of your model/statue.
Copper
Bronze
Marble Sheet Metal
Glass
Iron
Granite
Sheet Metal
PerspexExamples of how
different materials are used to create sculptures
Costs
In the table below are the costs of a selection of materials, from which you may choose to make your model/statue. They have been split into whether you need to calculate the volume or the surface area
VOLUME SURFACE AREA
Copper £3 per Kg(Density of Copper is 8930 kg/cubic metre)
Marble £59.50 + VAT per square metre
Iron £4 per Kg(Density of Iron is 7850 kg/cubic metre)
Granite £25 + VAT per square metre
Bronze £3.65 per Kg(Density of Bronze is 8430 kg/cubic metre)
Sheet Metal £11.25 per square metre
Perspex £7.88 per square metre
Glass £23.50 per square metre
N.B. Where the cost has been given in terms of weight (i.e per Kg), you will need to use the density of the material in your calculations.
Chosen material is Chosen material is
Total volume =Remember that you will need to submit additional calculations
to support this
Total surface area =Remember that you will need to submit additional calculations
to support this
Cost of statue =Remember that you will need to submit evidence of how you
have costed your statue
Cost of statue =Remember that you will need to submit evidence of how you
have costed your statue
Please include any additional information or costings here
Please include any additional information or costings here
Please affix a photographof your model here Title of Submission:
Submitted by:
Materials to be used:Estimated amount of material required:(please provide calculations on a separate sheet)
Estimated cost of structure:
Please provide an explanation of the vision/story behind your choice of structure:
Fourth Plinth Submission
Formulae you may need to knowArea of:• Rectangle = length × width• Triangle = 1/2 base × height
• Circle = πr²• Trapezium = 1/2 (a + b) × vertical height
(where a and b are the two parallel sides)• Surface area of sphere = 4 πr²
Volume of:• Cuboid = length × width × height• Prism = area of cross-section × height• Cylinder = πr² h• Cone = 1/3 πr² h
• Pyramid = 1/3 × base area × height
• Sphere = 4/3 πr²
To find the surface area of a shape, find the area of each face and add them
together.
Enlarging your design to estimate materials needed and cost
To be able to estimate the quantity of materials needed and the costing involved, you first need to be able to work out the
enlarged dimensions.
General Rule
• If the lengths in a shape or solid are all multiplied by a scale factor of k, then the areas will be multiplied by a scale factor of k² and the volumes will be multiplied by a scale factor of k³.
• For example, if the lengths are enlarged with scale factor 4, then the areas will be enlarged with scale factor 16 and the volumes will be enlarged with scale factor 64.
Plan of action• Draw a sketch of the sculpture you would like to make• What polyhedra could you use to create your sculpture?• How much paper, card or other material will you need?
What other resources will you require?• Split the project up into individual tasks within your group
and decide who is responsible for each task• Work out how much it will cost to make your sculpture using
the costing sheet• Complete the submission form to bid for your sculpture to
appear on the plinth
Dodecahedron IcosidodecahedronTetrahedron
CubeOctahedron
Icosahedron Hexagonal prism
Pentagonal prism
Triangular prism
Octagonal prism
Cuboctahedron
Square based pyramid
Cuboid
Cylinder
Here are a selection of polyhedra you
may wish to consider in your planning
Cone
Sphere
Pyramids and ConesVolume = 1/3 x area of base x height
A few semi-regular polyhedra
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