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GeometryLesson 1 – 7
Three-Dimensional Figures
Objective:Identify and name three-dimensional figures.
Find surface area and volume.
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PolyhedronsPolyhedronsA solid with all flat surfaces that enclose a
single region of space.
Face – each flat surface
Edges – the line segment where the faces intersect
Vertex – the point where 3 or more edges intersect
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Types of Solids:Prism
A polyhedron with 2 parallel and congruent faces called bases
Bases are connect by parallelogram faces
This is one example of a prism
Named using the bases:
Pentagonal Prism
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Naming Prisms
Triangular Prism
RectangularPrism
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Types of Solids:Pyramid
A polyhedron that has a polygonal base and three or more triangular faces that meet at a common point.
One example:
Rectangular Pyramid
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Naming Pyramids
TriangularPyramid
RectangularPyramid
PentagonalPyramid
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Types of Solids:Cylinder
Not a polyhedron
A solid with congruent parallel circular bases connected by a curved surface.
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Types of Solids:Cone
Not a polyhedron
A solid with a circular base connected by a curved surface to a single vertex.
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Types of Solids:Sphere
Not a polyhedron
A set of points in space that are the same distance from a given point. A sphere has no faces, edges, or vertices.
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Determine whether the solid is a polyhedron, if yes, name the bases,
faces, edges, and vertices.
Yes a polyhedronBases: MNOP & RSTQ
*Use the ‘top’ and ‘bottom’ on Rectangular prisms for the bases.
Faces: MNOP, RSTQ, MRQP, RSNM, STON, PQTO
Edges: QPTOSNRM
RQMPPOQTNOSTRSMN
Vertices: R, M, S, N, T, O, Q, P
Remember to include the bases
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Determine whether the solid is a polyhedron, if yes, name the bases,
faces, edges, and vertices.
Not a polyhedron
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Determine whether the solid is a polyhedron, if yes, name the bases,
faces, edges, and vertices.
Bases: GHI & JKL
Faces: GHKJ, HKLI, & GJLI
Vertices: G,H,K,J,L,I
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Regular Polyhedron
A polyhedron with all faces regular polygons and all edges congruent.
Can you think of a regular polygon?
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Regular Polyhedrons:Platonic Solids
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Regular Polyhedrons:Platonic Solids
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Area & VolumeLateral Area – area of the lateral faces (faces that are not bases)
Surface Area (Total Area)– is the area of the whole figureLateral area + area of bases
Volume – the measure of the amount of space enclosed by a solid figure.
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Hands-on Activity
Using the geometric solids set
Find formulas for the following for all solidsLateral AreaSurface Area (Total Area)Volume
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Find Surface area and Volume
Square Pyramid
Surface area (Total Area): write formula first
BPT 2
1
365242
1TFind P and B first
P = 4(6) = 24B = 6*6 = 36
Plug into formula
= 96 cm2
Continued…
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Continued…Volume
BhV
3
1
Remember B = 36
4363
1V
= 48 cm3
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Find Surface area & Volume 222 rrhT
2621862
hrV 2 186 2
72216 2288 cm
28.904 cmNeed to have both! 648
38.2035 cmNeed to have both!
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Find Surface Area & Volume
BPhT 2P = 2(5.2) + 2(10) = 30.4B = (5.2)(10) = 52
T = (30.4)(6) + 2(52)= 286.4 cm2 V = Bh
= (52)(6)= 312 cm3
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Find the Surface Area & Volume
2rrT 2151715
225255 2480 in
20.1508 in1507.96 rounded up to 1508.0
hrV 2
3
1
8153
1 23600 in
30.1885 in1884.95 rounded up
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The diameter of the pool Mr. Sato purchased is 8 feet. The height of the pool is 20 inches. Find each measure to the nearest tenth.
Surface Area of pool
222 rrhT
243
2142
*Be careful dealing with feet and inches!
20 inches is 1 2/3 feet
163
113
insq
insq
2.923
129
We don’t need 2 bases since the pool Does not have a top
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Volume of water needed to fill the pool to a depth of 16 inches.
hrV 2Be careful with feet and inches!
3
114 2V 16 inches is 1 1/3 feet
ftcubic
ftcubic
0.673
121