3-D Geometry - NJCTL

Slide 1 / 138

3-D Geometry

Slide 3 / 138

Slide 2 / 138

Table of Contents

3-Dimensional Solids Nets Volume

? Prisms and Cylinders ? Pyramids, Cones & Spheres

Surface Area

? Prisms ? Pyramids ? Cylinders ? Spheres

More Practice/ Review

Click on the topic to go to that section

Slide 4 / 138

3-Dimensional Solids

Return to Table of Contents

The following link will take you to a site with interactive 3-D figures and nets.

Slide 5 / 138

Polyhedron A 3-D figure whose faces are all polygons Sort the figures into the appropriate side.

Polyhedron

Not Polyhedron

Slide 6 / 138

3-Dimensional Solids

Categories & Characteristics of 3-D Solids:

Prisms

1. Have 2 congruent, polygon bases which are parallel

to 2.

oSnideeasnaorteherer ctangularc(lpicakratollerelovgeraal ms)

3. Named by the shape of their base

Pyramids 1. Have 1 polygon base with a vertex opposite it 2. Sides are triancgliuclkatro reveal 3. Named by the shape of their base

Slide 7 / 138

3-Dimensional Solids

Categories & Characteristics of 3-D Solids:

Cylinders 1. Have 2 congruent, circular bases which are parallel to oneclaicnkottoherreveal 2. Sides are curved

Cones 1. Have 1 circular bases with a vertex opposite it 2. Sides are curvceldick to reveal

Slide 8 / 138

3-Dimensional Solids

Vocabulary Words for 3-D Solids:

Polyhedron

Face Edge Vertex (Vertices)

A 3-D figure whose faces are all polygons (Prisms & Pyramids)

Flat surface of a Polyhedron

Line segment formed where 2 faces meet

Point where 3 or more faces/edges meet

Slide 9 / 138

Sort the figures. If you are incorrect, the figure will be sent back.

Slide 10 / 138

Slide 11 / 138

Slide 12 / 138

Slide 13 / 138

Slide 14 / 138

Slide 15 / 138

For each figure, find the number of faces, vertices and edges. Can you figure out a relationship between the number of faces, vertices and edges of 3-Dimensional Figures?

Name

Cube

Rectangular Prism

Triangular Prism

Triangular Pyramid

Square Pyramid

Pentagonal Pyramid

Octagonal Prism

Faces 6 6 5 4 5 6 10

Vertices 8 8 6 4 5 6 16

Edges 12 12 9 6 8 10 24

Slide 17 / 138

Slide 16 / 138 Euler's Formula

F + V - 2 = E

The numcbleicr kofteodrgeevseisal2 less than

the sum of the faces and vertices.

Slide 18 / 138

Slide 19 / 138

Slide 21 / 138 Nets

Nets are two-dimensional drawings that represent the surface area of three-dimensional shapes.

There is more than one way to draw a net for a cube, however not all nets can be folded into a cube...

Slide 23 / 138

click to reveal the cube flat patterns

Slide 20 / 138

Nets

Return to Table of Contents

Slide 22 / 138

Nets - Flat Patterns Activity Part 1 Cut arrangements of 6 squares out of grid paper. How many different arrangements can be folded into a cube? Hint: You just saw one arrangement that works and one that does not.

see next page for answers...

Slide 24 / 138

Nets - Flat Patterns Activity Part 2

Cut an arrangement out of grid paper to create a rectangular prism that is not a cube .

Now make another flat pattern for the same rectangular prism.

Try each pattern out by folding it into a box.

What are the dimensions of each face of your rectangular prism?

Slide 25 / 138

Nets for prisms will have rectangular faces and two bases for which the shape is named. Notice the two triangles are opposite from one another (bases).

Slide 27 / 138

Slide 26 / 138 Slide 28 / 138

Slide 29 / 138

Slide 30 / 138

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download