| A | B |
|---|
| Polyhedron | is a solid that is bounded by polygons |
| Euler’s Theorem | The number of faces (F), vertices (V), and edges (E) of a polyhedron is related by: F + V=E + 2 |
| Surface | a surface of a polygon consists of all points on its faces |
| Convex Polyhedron | a polyhedron is convex if any two points on its surface can be connected by a line segment that lies entirely inside of on the polyhedron |
| Regular Polyhedron | a polygon is regular if all its faces are congruent regular polygons |
| prism | a polyhedron that has two parallel, congruent faces called bases. The other faces, called lateral faces, are parallelograms and are formed by connecting corresponding vertices of the bases |
| Right Prism | a prism in which each lateral edge is perpendicular to both bases |
| Oblique Prisms | are prisms that have lateral edges that are oblique to the bases |
| Surface area | of a polyhedron is the sum of the areas of its faces |
| Surface Area of a Right Prism | The surface area, S, of a right prism is: S = 2B + Ph, where B is the area of the base, P is the perimeter of a base, and h is the height |
| Surface Area of a Right Cylinder | The surface area, S, of a right cylinder is S = 2B + Ch where B, is the area of the base, C is the circumference of a base, and h is the height. |
| Pyramid | is a polyhedron in which the base is a polygon and the lateral faces are triangles that have a common vertex. |
| Regular Pyramid | a pyramid is regular if its base is a regular polygon and if the segment from the vertex to the center of the base is perpendicular to the base |
| Surface Area of a Regular Pyramid | The surface area, S of a regular pyramid is S = b + 1/2Pl, where B is the area of the base, P is the perimeter of the base, and l is the slant height. |
| Circular Cone | or a cone is a solid that has a circular base and a vertex that is not in the same plane as the base. |
| Right Cone | is a cone in which the vertex lies directly above the base |
| Surface Area of a Right Cone | The surface area, S, of a right cone is Pi times the radius squared plus Pi times the radius times the slant height |
| Volume of Cube Postulate | The volume of a cube is the cube of the length of its side |
| Volume Congruence Postulate | If two polyhedrons are congruent, then they have the same volume |
| Volume Addition Postulate | The volume of a solid is the sum of the volumes of all its non-overlapping parts. |
| Cavalieri’s Priniple | If two solids have the same height and the same cross-sectional area at every level, then they have the same volume |
| Volume of a Prism | The volume, V, of a prism is V = Bh, where B is the area of a base and h is the height |
| Volume of a Cylinder | The volume, V, of a cylinder is V = Bh where B is the area of the base, h is the height, |
| Volume of a Pyramid | The volume, V, of a pyramid is given by V = 1/3Bh, where B is the area of the base and h is the height. |
| Volume of a Cone | The volume, V, of a cone is given by V =1/3Bh where B is the area of the base, and h is the height |
| Sphere | is the set of all points in space that are a given distance, r, from a point called the center. |
| Radius | the distance, r, in a sphere is the radius |
| Chord | of a sphere is a segment whose endpoints are on the sphere |
| Diameter | of a sphere is a chord that contains its center |
| Great Circle | if the plane contains the center of the sphere, then the intersection is the great circle |
| Hemispheres | each great circle of a sphere separates a sphere into two congruent halves called hemispheres |
| Surface area of a Sphere | The surface area, S, of a sphere of radius r is 4 tims Pi times the radius squared |
| Volume of a Sphere | The volume, V, of a sphere of radius r is 4/3 times Pi times the radius cubed |
