11 4 Vocabulary Polyhedron Prism Pyramid Cylinder Cone

11. 4 Vocabulary Polyhedron Prism, Pyramid, Cylinder, Cone, Sphere lateral face/lateral edge base/base edge vertex altitude cross section solid of revolution axis or revolution

A polyhedron is formed by four or more polygons that intersect only at their edges. Prisms and pyramids are polyhedrons, but cylinders, cones and spheres are not.

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Prisms and Pyramids are named by their base(s):

11. 4 Supplemental The following materiel is not in section 11. 4 of the textbook. Parts of this materiel are included in sections 11. 5/6/7. You are responsible for this supplemental information. Vocabulary: Right/Oblique (Prisms-Pyramids-Cones) Surface Area Lateral Surface Area Base Area

Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face.

An altitude/height of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude. h Surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral pieces.

Right Prisms and Cylinders: Flat-Tops Rt Cylinder Lateral Surface Area: L = Ph P is the Perimeter of the Base, h is the height Surface Area: S = L + 2 B B is Area of the Base

Example 1 A: Prisms Find the lateral area and surface area of the right rectangular prism. Round to the nearest tenth, if necessary. Note: Always draw the base to find P and B

Example 2 A: Right Cylinder Find the lateral area, and surface area of the right cylinder. Give your answers in terms of .

Find the lateral area and surface area of each figure. Round to the nearest tenth, if necessary. 1. a cube with edge length 10 cm L = 400 cm 2 ; S = 600 cm 2 2. a regular hexagonal prism with height 15 in. and base edge length 8 in. L = 720 in 2; S 1052. 6 in 2 3. a right cylinder with base area 144 cm 2 and a height that is the radius L 301. 6 cm 2; S = 1206. 4 cm 2

Right Pyramids and Cones: Pointy-Tops l h r Right Cone Lateral Surface Area: L = ½ Pl P is the Perimeter of the Base, l is the Slant Height Surface Area: S = L + B B is Area of the Base

Triangles “In” Pyramids

Given a square base pyramid, h = 12, l = 13, s = 10, find L, and S Find L, and S of the cone with r = 8, slant height = 10.