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1.7: Three-Dimensional Figures
GEOMETRY
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Polyhedron - a solid with all flat surfaces that enclose a single region of space
Face – each flat surface
Edges- line segments where faces intersect
Vertex- where three or more edges intersect
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TYPES OF SOLIDS: POLYHEDRONS
Prism- polyhedron with two parallel congruent faces called bases connected by parallelogram faces
Pyramid – polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex
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Cylinder- solid with congruent parallel circular bases connected by a curved surface.
Cone- solid with a circular base connected by a curved surface to a single vertex.
Sphere- set of all point in space that are the same distance from a given point. Has no faces, edges, or vertices.
TYPES OF SOLIDS: NOT POLYHEDRONS
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Regular polyhedron- all of its faces are regular congruent polygons and all of its edges are congruent
There are exactly 5 types They are called the Platonic
solids.
Tetrahedron, Hexahedron (Cube), Octahedron, Dodecahedron, Icosahedron
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Surface area- 2 dimensional measurement of the surface of a solid figure
“to wrap all the way around it”
Volume – measure of the amount of space enclosed by a solid
“fill it up”
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Prism Regular Pyramid
Cylinder Cone Sphere
Surface Area
T= Ph+2B
T=1/2Pl + B
T=2πrh + 2πr2
T=πrl +πr2
T=4πr2
Volume
V= Bh V= 1/3Bh V=πr2h V= 1/3πr2
h
V= 4/3πr3
T= total surface area V=volume h= height of solidP= Perimeter of base B=area of base l= slant height, r=radius
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Homework
Page 70: 1-25 odds, 47-52 all