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Transcript of 8-4
8-4 Drawing Three-Dimensional Figures
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm Up
Course 3
8-4 Drawing Three-Dimensional Figures
Find the circumference of each circle, both in terms of and to the nearest tenth. Use 3.14 for .
1. radius 2.5 m
2. diameter 8.8 cm
3. radius 14 ft
Find the area of each circle, both in terms of and to the nearest tenth. Use 3.14 for .
4. diameter 14 ft
196ft2; 615.4 ft2
5m; 15.7 m
8.8cm; 27.6 cm
49ft2; 153.9 ft2
Problem of the DayWhat is the least number of lines needed to draw 5 squares ?
6
Course 3
8-4 Drawing Three-Dimensional Figures
Learn to draw and identify the parts of three-dimensional figures.
Course 3
Drawing 3 Dimensional Figures
Course 3
8-4 Drawing Three-Dimensional Figures
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.
Course 3
8-4 Drawing Three-Dimensional Figures
Edge
Face
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.
Vertex
Course 3
8-4 Drawing Three-Dimensional Figures
Name the vertices, edges, and faces of the three-dimensional figure shown.
Additional Example 1: Identifying Vertices, Edges, and Faces
The vertices are: S, T, U, V, W, X.
The faces are triangles UTX and VSW and rectangles VSTU, SWXT, VWXU.
Course 3
8-4 Drawing Three-Dimensional Figures
U
T
X
V
S
WThe edges are : VS, SW, WV, UT, TX, XU, VU, ST, and WX.
___ ______
___ ______ ___ ___ ___
Name the vertices, edges, and faces of the three-dimensional figure shown.
Check It Out: Example 1
The vertices are: A, B, C, D, E, F, G, H.
The faces are squares ADHE and BCGF and rectangles ABCD, HGCD, EFGH, and EFBA.
Course 3
8-4 Drawing Three-Dimensional Figures
A
D
FB
C
G
E
HThe edges are : AD, DC, CB, BA, AE, EF, FG, GC, BF, DH, HE, and GH.
___ ______
___ ______ ___ ___ ___
Draw the figure shown in front, top, and side views.
Additional Example 2: Drawing a Figure When Given Different Perspectives
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.
Course 3
8-4 Drawing Three-Dimensional Figures
Front Top Side
Draw the figure shown in front, top, and side views.
Check It Out: Example 2
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.
Course 3
8-4 Drawing Three-Dimensional Figures
Front Top SideFront
Side
Draw the front, top, and side views of the figure.
Additional Example 3: Drawing Different Perspectives of a Figure
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.
Course 3
8-4 Drawing Three-Dimensional Figures
Front
Front:
Draw the front, top, and side views of the figure.
Additional Example 3 Continued
The figure looks like a row of 3 squares.
Course 3
8-4 Drawing Three-Dimensional Figures
Top
Top:
Draw the front, top, and side views of the figure.
Additional Example 3 Continued
The figure looks like a column of 3 squares.
Course 3
8-4 Drawing Three-Dimensional Figures
Side
Side:
Draw the front, top, and side views of the figure.
Check It Out: Example 3
The figure looks like a row of 4 squares on the bottom with 2 squares on top.
Course 3
8-4 Drawing Three-Dimensional Figures
Front
Front:
Draw the front, top, and side views of the figure.
Check It Out: Example 3 Continued
The figure looks like a row of 4 squares.
Course 3
8-4 Drawing Three-Dimensional Figures
Top
Top:
Draw the front, top, and side views of the figure.
Check It Out: Example 3 Continued
The figure looks like a column of 2 squares.
Course 3
8-4 Drawing Three-Dimensional Figures
Side:
Side