Geometric Solids and Surface Area Geometry Regular Program SY 2014-2015 Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson
Jan 04, 2016
Geometric Solids and Surface Area
Geometry Regular ProgramSY 2014-2015
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson
The Geometric Solids
Observe that these have
CURVED surfaces.
These DO NOT have CURVED
surfaces.
The Geometric Solids
Observe that these also
have CURVED surfaces.
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
Classification of Polyhedra
Polyhedra are classified according to the number of faces
6 faces 7 faces 10 faces
Classification of Polyhedra
How many faces does a tetrahedron have ?
REGULAR POLYHEDRON – a
polygon whose faces are congruent regular
polygons
Which are polyhedra?
PRISM Has 2 parallel & congruent bases
base
base
Other faces are LATERAL faces,
which are parallelograms
LATERAL EDGES
PRISM
- classified according to base
PRISMRIGHT vs OBLIQUE
Lateral faces are rectangles.
Lateral faces: NOT rectangles.
CYLINDER Has 2 parallel & congruent bases
base
base
LATERAL face
CYLINDERRIGHT vs OBLIQUE
Axis is perpendicular to the circular base.
Axis is NOT perpendicularto the circular base.
PYRAMIDHas only 1 base
base
LATERAL faces are triangles.
LATERAL EDGES
Vertex of pyramid
PYRAMID In a pyramid, there is a “slant height”.
The slant height is the height of a triangular
face.
PYRAMID- classified according to base
Which of these pyramids are
right? Oblique?
CONEHas only 1 base
base LATERAL face
Vertex of cone
Slant height
Height of cone
CONERIGHT vs OBLIQUE
SPHERE
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?
Exercises What solid is illustrated? Be specific.
Exercises What solid is illustrated? Be specific.
Exercises What solid is illustrated? Be specific.
Exercises What solid is illustrated? Be specific.
Conservatories in Edmonton, Canada Containers in an ice
cream plant in Burlington, Vermont
Exercises What solid is illustrated? Be specific.
A bag of oranges
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.
SURFACE AREA
Example A:
STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.
SURFACE AREA
Solution:
SURFACE AREA
Solution:
SURFACE AREA
Example B:
STRATEGY!1.Draw each face.2.Get area of each face.3.Add all areas.
SURFACE AREA
Solution:
SURFACE AREA
Solution:
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!
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
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
SURFACE AREA
SURFACE AREA
Example D:
How about the surface area of a cone?
Lateral face is a sector!
SURFACE AREA
Total SA = Lateral Area +
Base Area
PRISM +
CYLINDER
+
PYRAMID
+
CONE +
SURFACE AREA
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve for the surface area of each given solid
Exercises on Surface AreaSolve.
MORE Exercises on Surface AreaSolve for the SA.
Exercises on Surface AreaSolve.
Exercises on Surface AreaSolve.
MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)
MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)
MORE Exercises on Surface AreaExpress the SA of each solid (no answers given)
MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)
MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)
MORE Exercises on Surface AreaSolve for the surface area of each solid (no answers given)
MORE Exercises on Surface AreaSolve for the SA of each solid (no answers given)