geometric solids and surface area geometry regular program sy 2014-2015 sources: discovering...
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![Page 1: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/1.jpg)
Geometric Solids and Surface Area
Geometry Regular ProgramSY 2014-2015
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson
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The Geometric Solids
Observe that these have
CURVED surfaces.
These DO NOT have CURVED
surfaces.
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The Geometric Solids
Observe that these also
have CURVED surfaces.
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The Geometric Solids
A solid formed by polygons that enclose a single region of space is
called a POLYHEDRON (pl. polyhedra)
FACE – each polygonal surfaceEDGE – segment where 2 polygons
intersectVERTEX – point where 3 or more edges
intersect
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Classification of Polyhedra
Polyhedra are classified according to the number of faces
6 faces 7 faces 10 faces
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Classification of Polyhedra
How many faces does a tetrahedron have ?
REGULAR POLYHEDRON – a
polygon whose faces are congruent regular
polygons
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Which are polyhedra?
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PRISM Has 2 parallel & congruent bases
base
base
Other faces are LATERAL faces,
which are parallelograms
LATERAL EDGES
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PRISM
- classified according to base
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PRISMRIGHT vs OBLIQUE
Lateral faces are rectangles.
Lateral faces: NOT rectangles.
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CYLINDER Has 2 parallel & congruent bases
base
base
LATERAL face
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CYLINDERRIGHT vs OBLIQUE
Axis is perpendicular to the circular base.
Axis is NOT perpendicularto the circular base.
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PYRAMIDHas only 1 base
base
LATERAL faces are triangles.
LATERAL EDGES
Vertex of pyramid
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PYRAMID In a pyramid, there is a “slant height”.
The slant height is the height of a triangular
face.
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PYRAMID- classified according to base
Which of these pyramids are
right? Oblique?
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CONEHas only 1 base
base LATERAL face
Vertex of cone
Slant height
Height of cone
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CONERIGHT vs OBLIQUE
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SPHERE
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HEMISPHERE: Half a sphere PLUS the circular baseThe circle that
encloses the base is the GREAT
CIRCLE.
If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-
section?
If a plane cuts a sphere along the center, then the
plane contains the great circle.
Is the equator In a globe a great circle?
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Exercises What solid is illustrated? Be specific.
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Exercises What solid is illustrated? Be specific.
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Exercises What solid is illustrated? Be specific.
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Exercises What solid is illustrated? Be specific.
Conservatories in Edmonton, Canada Containers in an ice
cream plant in Burlington, Vermont
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Exercises What solid is illustrated? Be specific.
A bag of oranges
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What is SURFACE AREA?The surface area of any
given solid is the SUM of the areas of ALL EXPOSED and TANGIBLE faces that enclose the
solid.
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SURFACE AREA
Example A:
STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.
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SURFACE AREA
Solution:
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SURFACE AREA
Solution:
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SURFACE AREA
Example B:
STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.
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SURFACE AREA
Solution:
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SURFACE AREA
Solution:
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SURFACE AREA
Example C:
How do we get the surface area of a pyramid?
STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.
Get area of TRIANGLES and the area of the BASE!
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SURFACE AREA
Example C: The pyramid has a square base with perimeter 48, and a height of 8 cm.
8
1212
6
slant height
10
10
12
Total SA = 4 Congruent Triangular Faces + 1 square
12
12
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SURFACE AREA
Example D:
Is there a formula to get the surface area of a right pyramid with a regular base?
Solution:
Lateral Area + Base Area
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SURFACE AREA
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SURFACE AREA
Example D:
How about the surface area of a cone?
Lateral face is a sector!
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SURFACE AREA
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Total SA = Lateral Area +
Base Area
PRISM +
CYLINDER
+
PYRAMID
+
CONE +
SURFACE AREA
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Exercises on Surface AreaSolve for the surface area of each given solid
![Page 40: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/40.jpg)
Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
![Page 45: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/45.jpg)
Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
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Exercises on Surface AreaSolve for the surface area of each given solid
![Page 50: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/50.jpg)
Exercises on Surface AreaSolve for the surface area of each given solid
![Page 51: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/51.jpg)
Exercises on Surface AreaSolve for the surface area of each given solid
![Page 52: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/52.jpg)
Exercises on Surface AreaSolve for the surface area of each given solid
![Page 53: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/53.jpg)
Exercises on Surface AreaSolve for the surface area of each given solid
![Page 54: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/54.jpg)
Exercises on Surface AreaSolve.
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MORE Exercises on Surface AreaSolve for the SA.
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Exercises on Surface AreaSolve.
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Exercises on Surface AreaSolve.
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MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)
![Page 59: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/59.jpg)
MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)
![Page 60: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/60.jpg)
MORE Exercises on Surface AreaExpress the SA of each solid (no answers given)
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MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)
![Page 62: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/62.jpg)
MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)
![Page 63: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/63.jpg)
MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)
![Page 64: Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson](https://reader035.vdocuments.net/reader035/viewer/2022062721/56649f225503460f94c3b8ba/html5/thumbnails/64.jpg)
MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)