Concept

Polyhedron 

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

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.

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

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.

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

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.

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 TVertex: Wno faces or edges

A. A

B. B

C. C

D. D

A. triangular pyramid

B. pentagonal prism

C. rectangular prism

D. square pyramid

A. Identify the solid.

A. A

B. B

C. C

D. D

A. cone

B. cylinder

C. pyramid

D. polyhedron

B. Identify the solid.

A. A

B. B

C. C

D. D

A. triangular prism

B. triangular pyramid

C. rectangular pyramid

D. cone

C. Identify the solid.

Find Surface Area and Volume

Find the surface area and volume of the cone.

π π

.

Find Surface Area and Volume

r = 3, h = 4

Volume of a cone

Simplify.

A. A

B. B

C. C

D. D

A. surface area = 288 ft2

volume = 336 ft3

B. surface area = 336 ft2

volume = 288 ft3

C. surface area = 26 ft2

volume = 60 ft3

D. surface area = 488 ft2

volume = 122 ft3

Find the surface area and volume of the triangular prism.

Surface Area and Volume

A. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters andarchitectural 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.

Surface Area and Volume

Surface area of a cylinder

r = 1.875 in., h = 32 in.

Answer: Mike needs about 399.1 square inches ofcardboard to make the tube.

Use a calculator.399.1

Surface Area and Volume

B. CONTAINERS Mike is creating a mailing tubewhich can be used to mail posters andarchitectural plans. The diameter of the base is

inches, and the height is feet. Find the

volume of the tube.

Volume of a cylinder

r = 1.875 in., h = 32 in.

Use a calculator.353.4

A. A

B. B

C. C

D. D

A. surface area = 2520 in2

B. surface area = 18 in2

C. surface area = 180 in2

D. surface area = 1144 in2

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

A. volume = 1144 in3

B. volume = 14 in3

C. volume = 2520 in3

D. volume = 3600 in3

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.