Chapter 1.7 and 12.1 Thee-Dimensional Figures and their representations

Vocabulary Polyhedron – a solid with all flat surfaces that enclose a single region of

space

Face – each flat surface of a polyhedron

Edges – the line segments where faces intersect

Vertex – the point where three or more edges intersect

Example 1Identify 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 1Identify 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

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

A. triangular pyramid

B. pentagonal prism

C. rectangular prism

D. square pyramid

A. Identify the solid.

A. cone

B. cylinder

C. pyramid

D. polyhedron

B. Identify the solid.

A. triangular prism

B. triangular pyramid

C. rectangular pyramid

D. cone

C. Identify the solid.

Concept

Cross Section A cross section is the intersection

of a solid and a plane

Example 3Identify Cross Sections of Solids

BAKERY A customer ordered a two-layer sheet cake. Determine the shape of each cross section of the cake below.

Example 3

A. Cut the cone parallel to the base.

B. Cut the cone perpendicular to the base through the vertex of the cone.

C. Cut the cone perpendicular to the base, but not through the vertex.

D. Cut the cone at an angle to the base.

A solid cone is going to be sliced so that the resulting flat portion can be dipped in paint and used to make prints of different shapes. How should the cone be sliced to make prints in the shape of a triangle?