Concept Polyhedron A solid with four or more flat surfaces that are polygonal regions.

Concept

Example 1 Identify Solids A. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1 Identify Solids The solid is formed by polygonal faces, so it is a polyhedron. The bases are rectangles. This solid is a rectangular prism. Answer:rectangular prism; Bases:rectangles EFHG, ABDC Faces:rectangles FBDH, EACG, GCDH, EFAB, EFGH, ABCD Vertices:A, B, C, D, E, F, G, H

Example 1 Identify Solids B. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1 Identify Solids The solid is formed by polygonal faces, so it is a polyhedron. The bases are hexagons. This solid is a hexagonal prism. Answer: hexagonal prism; Bases:hexagon EFGHIJ and hexagon KLMNOP Faces:rectangles EFLK, FGML, GHMN, HNOI, IOPJ, JPKE Vertices: E, F, G, H, I, J, K, L, M, N, O, P

Example 1 Identify Solids C. Determine whether the solid is a polyhedron. Then identify the solid. If it is a polyhedron, name the bases, faces, edges, and vertices.

Example 1 Identify Solids The solid has a curved surface, so it is not a polyhedron. The base is a circle and there is one vertex. So, it is a cone. Answer: Base: circle T Vertex: W no faces or edges

A.A B.B C.C D.D Example 1 A.triangular pyramid B.pentagonal prism C.rectangular prism D.square pyramid A. Identify the solid.

A.A B.B C.C D.D Example 1 A.cone B.cylinder C.pyramid D.polyhedron B. Identify the solid.

A.A B.B C.C D.D Example 1 A.triangular prism B.triangular pyramid C.rectangular pyramid D.cone C. Identify the solid.

Concept

Example 2 Find Surface Area and Volume Find the surface area and volume of the cone. π π.

Example 2 Find Surface Area and Volume r = 3, h = 4 Volume of a cone Simplify.

A.A B.B C.C D.D Example 2 A.surface area = 288 ft 2 volume = 336 ft 3 B.surface area = 336 ft 2 volume = 288 ft 3 C.surface area = 26 ft 2 volume = 60 ft 3 D.surface area = 488 ft 2 volume = 122 ft 3 Find the surface area and volume of the triangular prism.

Example 3 Surface Area and Volume A. CONTAINERS Mike is creating a mailing tube which can be used to mail posters and architectural plans. The diameter of the base is inches, and the height is feet. Find the amount of cardboard Mike needs to make the tube. The amount of material used to make the tube would be equivalent to the surface area of the cylinder.

Example 3 Surface Area and Volume Surface area of a cylinder r = in., h = 32 in. Answer:Mike needs about square inches of cardboard to make the tube. Use a calculator

Example 3 Surface Area and Volume B. CONTAINERS Mike is creating a mailing tube which can be used to mail posters and architectural plans. The diameter of the base is inches, and the height is feet. Find the volume of the tube. Volume of a cylinder r = in., h = 32 in. Use a calculator

A.A B.B C.C D.D Example 3 A.surface area = 2520 in 2 B.surface area = 18 in 2 C.surface area = 180 in 2 D.surface area = 1144 in 2 A. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the surface area of the box.

A.A B.B C.C D.D Example 3 A.volume = 1144 in 3 B.volume = 14 in 3 C.volume = 2520 in 3 D.volume = 3600 in 3 B. Jenny has some boxes for shipping merchandise. Each box is in the shape of a rectangular prism with a length of 18 inches, a width of 14 inches, and a height of 10 inches. Find the volume of the box.