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8-4. Drawing Three-Dimensional Figures. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 8-4. Drawing Three-Dimensional Figures. Course 3. Warm Up. Find the circumference of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p. 5  m; 15.7 m.

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8-4

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8-4

Drawing Three-Dimensional Figures

Warm Up

Problem of the Day

Lesson Presentation

Course 3

8-4

Drawing Three-Dimensional Figures

Course 3

Warm Up

Find the circumference of each circle, both in terms of p and to the nearest tenth. Use 3.14 for p.

5 m; 15.7 m

2. diameter 8.8 cm

8.8 cm; 27.6 cm

Find the area of each circle, both in terms of  and to the nearest tenth. Use 3.14 for .

196 ft2; 615.4 ft2

49 ft2; 153.9 ft2

4. diameter 14 ft

8-4

Drawing Three-Dimensional Figures

Course 3

Problem of the Day

What is the least number of lines needed to draw 5 squares ?

6

8-4

Drawing Three-Dimensional Figures

Course 3

Drawing 3 Dimensional Figures

Learn to draw and identify the parts of three-dimensional figures.

Course 3

8-4

Drawing Three-Dimensional Figures

Course 3

Vocabulary

face

edge

vertex

orthogonal views

8-4

Drawing Three-Dimensional Figures

Course 3

Three-dimensional figures have faces, edges, and vertices. A face is a flat surface, an edge is where two faces meet, and a vertex is where three or more edges meet.

8-4

Drawing Three-Dimensional Figures

Vertex

Edge

Face

Course 3

Since in a drawing of a three-dimensional object, you can only see up to three sides of a figure, you have to visualize how the figure looks from other angles. One way to do this is by drawing the orthogonal views of the figure. Orthogonal views show how the figure looks from the different perspectives, such as the front, side, and top views.

8-4

Drawing Three-Dimensional Figures

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The edges are : VS, SW, WV, UT, TX, XU, VU, ST, and WX.

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Course 3

Additional Example 1: Identifying Vertices, Edges, and Faces

Name the vertices, edges, and faces of the three-dimensional figure shown.

V

The vertices are: S, T, U, V, W, X.

U

S

W

T

X

The faces are triangles UTX and VSW and rectangles VSTU, SWXT, VWXU.

8-4

Drawing Three-Dimensional Figures

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The edges are : AD, DC, CB, BA, AE, EF, FG, GC, BF, DH, HE, and GH.

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Course 3

Check It Out: Example 1

Name the vertices, edges, and faces of the three-dimensional figure shown.

The vertices are: A, B, C, D, E, F, G, H.

F

E

B

A

H

G

D

C

The faces are squares ADHE and BCGF and rectangles ABCD, HGCD, EFGH, and EFBA.

8-4

Drawing Three-Dimensional Figures

Course 3

Additional Example 2: Drawing a Figure When Given Different Perspectives

Draw the figure shown in front, top, and side views.

Side

Front

Top

From the top and side views, there appears to be 3 cubes on the top level. The front view shows that the figure has six cubes.

8-4

Drawing Three-Dimensional Figures

Course 3

Check It Out: Example 2

Draw the figure shown in front, top, and side views.

Side

Side

Front

Top

Front

From the front and top views, there appears to be 1 cube on the bottom level. The side view shows that the bottom layer has cubes.

8-4

Drawing Three-Dimensional Figures

Front

Course 3

Additional Example 3: Drawing Different Perspectives of a Figure

Draw the front, top, and side views of the figure.

Front:

The figure looks like a row of 3 squares on the bottom with 2 squares on top of the right side and 1 square on top of the left side.

8-4

Drawing Three-Dimensional Figures

Top

Course 3

Draw the front, top, and side views of the figure.

Top:

The figure looks like a row of 3 squares.

8-4

Drawing Three-Dimensional Figures

Course 3

Draw the front, top, and side views of the figure.

Side:

The figure looks like a column of 3 squares.

Side

8-4

Drawing Three-Dimensional Figures

Course 3

Check It Out: Example 3

Draw the front, top, and side views of the figure.

Front:

The figure looks like a row of 4 squares on the bottom with 2 squares on top.

Front

8-4

Drawing Three-Dimensional Figures

Course 3

Check It Out: Example 3 Continued

Draw the front, top, and side views of the figure.

Top:

The figure looks like a row of 4 squares.

Top

8-4

Drawing Three-Dimensional Figures

Side

Course 3

Check It Out: Example 3 Continued

Draw the front, top, and side views of the figure.

Side:

The figure looks like a column of 2 squares.

8-4

Drawing Three-Dimensional Figures

Course 3

Lesson Quiz

1. Draw the figure shown in the front, top, and side views.

Front

Side

Top

Front

2. Draw the front and back views of the figure.

Front

Back