6th Grade Math Textbook, Fundamentals

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Write the name of the three-dimensional figure each object is most like.

4.Discuss and Write Imagine what a hexagonal prism looks like, then describe

it with words and a sketch. Count edges, vertices, and faces. Use Euler’s formula

to verify your counting.

Key Concept

For any polyhedron, if Fis the number

of faces, Eis the number of edges,

and Vis the number of vertices, then

FVE2.

Euler’s Formula

Lesson 11-1 for exercise sets.

There are also three-dimensional figures that have curved surfaces.

These include cylinders, cones, spheres, and hemispheres.

A has two circular

congruent bases that are parallel.

A is a figure with all points

the same distance from the center.

A has one circular base and

one curved surface that comes to a

point called the vertex.

sphere A hemisphereis half of a sphere.

cylinder cone

Building C is shaped like a cylinder.

You can use a formula known as Euler’s formula

to determine how many faces, edges, or vertices a

three-dimensional figure has.

Use this square prism to check Euler’s formula.

By counting, you can see that a square prism

has 6 faces, 8 vertices, and 12 edges.

Use Euler’s formula to check.

FVE 2 Euler’s formula

6  812  2 Substitute the known values.

14  14 Tr u e

?

6 faces

12 edges

8 vertices