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o 11.1 Drawing Views of Cube Structures

Use grid paper to draw top, front and side views of a cube structure.

You will need linking cubes.

1. This structure is built with five linking cubes. identify each view below as the top, front, or right side.

right side

front . • . • • '• •

2. Build each structure, and then draw it, using a thick line to indicate a change in depth.

mm a!

77 7

front front top right side

/ A

/ J <

/

) front front top right side

Top, front, and side views are used to represent a 3-D object with several drawings. To draw views of an object, you can: • Draw what you see when you

look at the structure straight on. • Look at the structure from a

slightly different angle to see changes in depth.

• Mark the changes in depth with a thick line.

For example, this structure would look as shown from the front, top, and side.

front top right side

92 Chapter 11: 3-D Geometry Copyright @ 2009 by Nelson Education Ltd.

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1 1 **y Building Cube Structures I mJL. from Views

] Make cube structures, given their top, front, and side views.

You will need linking cubes.

1. Which cube structure has these views?

a) 1

front top right side

I) ii)

ront front

fo)

L . J LJ LiL

front top right side

ii) /

7 front

front

iii) c A A

front

iii)

7 S s y j

front

C) I I I 1 i 1

front top right side

i) _ £ ii) /

front front

Copyright © 2009 by Nelson Education Ltd.

iii)

1 front

Chapter 11: 3-D Geometry 93

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11.3 Date:

Creating Isometric Drawings

You will need linking cubes.

1. Build and draw each cube structure.

I P A

J 1

• • ' ) front

o b)

< <

front

2. Build and draw two numbers from 2 to 9 with linking cubes.

o

An isometric drawing is a way to represent a 3-D object with a single drawing. You can create an isometric drawing of a cube structure by drawing the structure layer by layer, erasing hidden lines as you go. Or, you can line up the vertices (corners) of the cubes with the dots of the triangular dot paper. Start drawing a cube with three faces. Extend the lines to draw the cubes around it. Continue drawing the cubes until the isometric drawing matches the cube structure. For example, an isometric drawing for this structure is as shown:

/

•'

'J /

•'

'J /

) front

94 Chapter 11: 3-D Geometry Copyright © 2009 by Nelson Education Ltd.

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I yi Creating Cube Structures from • • Isometric Drawings

Create cube structures based on isometric drawings. J YOM wiN need timkm§ mho®.

1. Build two different cube structures to match this isometric drawing. Draw the back view of each structure to show how they are different.

2. Each set of drawings can be used to build the same structure. Which set would you use to build the structure? Explain your choice.

Drawing set A Drawing set B

top

1

X 1 j

X 1 j front top isometric

Copyright © 2009 by Nelson Education Ltd. Chapter 11: 3-D Geometry 95

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11.5 Rotating Cube Structures

Make and verify predictions about the views that result from rotating cube structures.

You w i l l irasedl Jinkiinig coaib-s®.

1. This cube structure is rotated vertically 90° cw. Draw the new front, top, and right side views.

front front top right side

2. Tell how the object was rotated from its original position in each case.

Original position

7\

Horizontally rotating an object means making it rotate like a merry-go-round. You can rotate an object clockwise (cw) or counterclockwise (ccw).This object has been rotated horizontally 90° ccw.

/ I

1

Vertically rotating an object means making it rotate like a Ferris wheel. You can rotate an object cw or ccw. This object has been rotated vertically 90° cw.

/ /"'• J V

/

P ' —

c)

96 Chapter 11: 3-D Geometry Copyright © 2009 by Nelson Education Ltd.

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11.6 Communicate about Views

Describe the views necessary to build a 3-D structure.

You will need linking cubes.

1. a) Build a cube structure with 10 linking cubes.

b) Draw the top, front, and side views of your structure.

front top right side

c) Create an isometric drawing of your structure.

S3 Did you provide enough information for someone else to complete each step correctly?

El Did you use drawings effectively?

Ei Did you use appropriate math language (e.g., rotation, horizontal, vertical)?

2. Explain to someone how to build the structure. Use the Communication Checklist to help you.

Copyright © 2009 by Nelson Education Ltd. Chapter 11: 3-D Geometry 97

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hapter Test Yourself

Circle the letter of the correct answer.

1. How many cubes ars in this structure?

A. 10

3. 13

C. 9

D. 12

Questions 2-4 are based on this cube structure

2. Select the top view.

A. SS.

3. Select the right view.

A.

4. Select the front view.

4 4 - IS.

i is V'i= -V..V.

5. Select the top view for this structure.

3.

__; .. . j

front

c. c.

In j

c.

-

c.

^

.j^ A

front

•

77

98 Chapter 11: 3-D Geometry Copyright © 2009 by Nelson Education Ltd.

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thai Test Yourself cont inued

S. Select the top view for this structure. I

r

front

C.

J. Select the right view for this structure.

front A. 1

—

3.

Select the top view for this structure.

1 front

13.

ID.

9" Iomr01,^ h ° r i Z O n t a ! i y C ! O C k W i S e ' * h ° W - V degrees was it rotated

Original position N e w p o s j t j o n

A, 30° B. 90°

Copyright © 2009 by Nelson Education Ltd.

C. 180° D. 360°

Chapter 11: 3-D Geometry