1.7: Three-Dimensional Figures

GEOMETRY

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

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

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

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

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”

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

Homework

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