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Chapter 12: Surface Area and Volume of Solids

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Page 1: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Chapter 12: Surface Area and Volume of

Solids

Page 2: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Polyhedron

• A solid that is bounded by polygons, called faces, that enclose a single region of space. • Plural is polyhedral or

polyhedrons

Page 3: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Face

• One of the flat surfaces that make a polyhedron.

Page 4: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Edge

• A line segment formed by the intersection of two faces of a polyhedron.

Page 5: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Vertex

• A point where three or more edges of a polyhedron meet.

Page 6: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Base

• One of two congruent faces of a polyhedron

Page 7: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Regular Polyhedron

• A convex polyhedron in which all of the faces are congruent regular polygons.

Page 8: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Convex Polyhedron

• A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron. If this segment goes outside the polyhedron, then the polyhedron is nonconvex or concave.

convex concave

Page 9: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Platonic Solids

• A convex polyhedron where every face is an identical regular polygon

Page 10: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Tetrahedron

• A polyhedron with four faces

Page 11: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Cube

• A polyhedron with six congruent square faces

Page 12: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Octahedron

• A polyhedron with eight faces

Page 13: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Dodecahedron

• A polyhedron with twelve faces

Page 14: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Icosahedron

• A polyhedron with twenty faces

Page 15: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Cross Section

• The intersection of a plane and a solid

Page 16: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Prism

• A polyhedron with two congruent faces called bases that lie in parallel planes.

Page 17: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Lateral Faces

• The faces of a prism that are parallelograms formed by connecting the corresponding vertices of the bases of the prism

Page 18: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Lateral Edges

• The segments connecting the corresponding vertices of the bases of a prism

Page 19: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Surface Area

• The sum of the areas of the faces of a polyhedron or other solid

Page 20: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Lateral Area

• The sum of the areas of the lateral faces of a polyhedron or other solid with one or two bases.

Page 21: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Net

• The two-dimensional representation of the faces of a polyhedron

Page 22: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Right Prism

• A prism in which each lateral edge is perpendicular to both bases

Page 23: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Stop for today.

Page 24: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Oblique Prism

• A prism with lateral edges that are NOT perpendicular to the bases

Page 25: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Cylinder

• A solid with congruent circular bases that lie in parallel planes

Page 26: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Right Cylinder

• A cylinder in which the segment joining the centers of the bases is perpendicular to both bases

Page 27: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Pyramid

• A polyhedron in which the base is a polygon and the lateral faces are triangles with a common vertex

Page 28: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Vertex of a Pyramid

• The common vertex of the triangles which make up the lateral faces of a pyramid.

Page 29: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Regular Pyramid

• A pyramid that has a regular polygon for a base and in which the segment joining the vertex and the center of the base is perpendicular to the base

Page 30: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Slant Height

• The height of a lateral face of the regular pyramid

Page 31: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Cone

• A solid that has one circular base and a vertex that is not in the same plane as the base

Page 32: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Vertex of a Cone

• The vertex that does not lie in the same plane as the base of a cone

Page 33: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Right Cone

• A cone in which the segment joining the vertex and the center of the base is perpendicular to the base. The slant height is the distance between the vertex and a point on the base edge.

Page 34: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Lateral Surface

• Consists of all segments that connect the vertex with points on the edge of the base.

Page 35: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Volume

• The number of cubic units contained in the interior of a solid

Page 36: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Sphere

• The set of all points in space equidistant from a given point called the center of the sphere

Page 37: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Center

• The center of a polygon’s circumscribed circle

Page 38: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Radius

• A segment whose endpoints are the center of the circle and a point on the circle. The distance from the center of a circle to any point on the circle.• Plural is radii

Page 39: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Chord

• A segment whose endpoints are on a sphere

Page 40: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Diameter

• A chord that contains the center of a sphere

Page 41: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Great Circle

• The intersection of a sphere and a plane that contains the center of the sphere

Page 42: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Hemisphere

• Half of a sphere, formed when a great circle separates into two congruent halves

Page 43: Chapter 12: Surface Area and Volume of Solids. Polyhedron A solid that is bounded by polygons, called faces, that enclose a single region of space. Plural

Similar Solids

• Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii