(1) Page #2 26 Even. (2) Page 596 #1 14. (3) Page #15 25 ; FF #26 and 28. (4) Page 603 #1 18. (5) Page #19 26
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1 Geometry/Trigonometry Unit 10: Surface Area and Volume of Solids Notes Name: Date: Period: # (1) Page #2 26 Even (2) Page 596 #1 14 (3) Page #15 25 ; FF #26 and 28 (4) Page 603 #1 18 (5) Page #19 26 (6) Page 610 #1 8 (7) Page #9 16, (8) Page 617 #1 9 (9) Page 617 #10 17 (10) Page 623 #1 12 (11) Page 623 #13-20 (12) Page #9-16 (13) Page 637 #1 20 All
2 Geometry Notes 12.1 Exploring Solids A is a solid that is bounded by polygons called, that enclose a single region of space. An of a polyhedron is a formed by the of. A of a polyhedron is a point where meet. These are NOT Polyhedrons These are Polyhedrons Theorem 12.1 Euler s Theorem: The number of faces (F), vertices (V), and edges (E) of a polyhedron is related by F + V = E + 2 The of a polyhedron consists of on its. A polyhedron is if any on its surface can be by a line that lies entirely the polyhedron. Convex Polyhedrons NonConvex Polyhedrons A polyhedron is if all its faces are and the at each vertex in. There are only of them. is one whose faces are of regular polygon and whose are all exactly the. Geometry Notes 12.2 Surface Area of Prisms and Cylinders A is a faces called. polyhedron that has
3 The other faces, called, are and are formed by connecting corresponding vertices of the bases. The connecting these corresponding vertices are. The, or height, of a prism is the between. In a, each is to both. that have lateral edges that are to the bases are oblique prisms. The of the is the of the prism. are classified by. The of a polyhedron is the of the of its. Theorem 12.2 The Surface Area of a Right Prism: perimeter of a base and H is the height., where B is the area of a base, P is the A circular cylinder (or simply ) is a solid with that lie in. The, or height, of a cylinder is the between its. The of a cylinder is the of its. A cylinder is if the of its is to its bases. Theorem 12.3 Surface Area of a Right Cylinder:, where B is the area of a base, C is the circumference of a base, r is the radius of a base, and h is the height. Or
4 Geometry Notes 12.3 Surface Area of Pyramids and Cones A is a polyhedron in which the and the are that have a common vertex. The of two lateral faces is a. The of the base and a lateral face is a. The, or height, of the pyramid is the between the and the. A pyramid is if its is a and if the segment from the to the of the base is to the. The of a regular pyramid is of any. A has no slant height. Theorem 12.4 Surface Area of a Regular Pyramid: perimeter of the base and l is the slant height., where B is the area of the base, P is the A circular cone, or simply, is a solid that has and a that is in the same. The consists of all that connect the with points on the. The, or height, of a cone is the between the and the plane that.
5 A right cone is one in which the lies of the base. The of a right cone is the distance between the and a. Theorem 12.5 Surface Area of a Right Cone: the slant height of the cone., where r is the radius of the base and l is Geometry Notes 12.4 Volume of Prisms and Cylinders One can think of the of a polyhedron as the number of contained in its. Volumes are measured in. Postulate 25 Volume of Cube Postulate: The volume of a cube is the cube of the length of its side, or E1. Postulate 26 Volume Congruence Postulate: If two polyhedrons are congruent then they have the same volume. Postulate 27 Volume Addition Postulate: The volume of a solid is the sum of the volumes of all its nonoverlapping parts. Theorem Cavalieri s Principle: If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
6 Theorem 12.7 Volume of a Prism:, where B is the area of the base and h is the height. Theorem 12.8 Volume of a Cylinder: radius of the base. Or., where B is the area of a base, h is the height and r is the Geometry Notes 12.5 Volume of Pyramids and Cones Theorem 12.9 Volume of a Pyramid:, where B is the area of the base and h is the height. Theorem Volume of a Cone: the radius of the base. Or, where B is the area of the base, h is the height, and r is These theorems to all pyramids and cones, both regular and.
7 Geometry Notes 12.6 Surface Area and Volume of Spheres A is the set of all points in that are a given distance, r, from a point called the. The distance,, is the of the sphere. The term also refers to any whose are the of the sphere and a. A of a sphere is a whose are. A of a sphere is a that contains its. All of a sphere have the, and this length is called the sphere s diameter. The diameter is twice the radius. If a a sphere, the will either be a single or a. If the contains the of a sphere, then the is a of the sphere. Each of a sphere a sphere into two congruent halves called. Theorem Surface Area of a Sphere:, where r is the radius Theorem Volume of a Sphere:, where r is the radius Geometry Notes 12.7 Similar Solids Two solids are if the of their (such as height or radii) are. This common is called the of one solid to the other solid. Any two cubes are similar and so are any two spheres. Theorem If two solids are similar with a scale factor of, then the corresponding areas have a ratio of and corresponding volumes have a ratio of
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