3-D Views of Solid Figures

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3-D Views of Solid Figures. Lesson 10-2. Different Views. Perspective view of a cone. Different angle views of a cone. the side (or from any side view). the top. the bottom. Example: Different Views. Front. Left. Right. Back. Top.

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3-D Views of Solid Figures

Lesson 10-2

Lesson 10-2: 3-D Views of Solid Figures

Different Views

Perspective view of a cone

Different angle views of a cone

the side

(or from any side view)

the top

the bottom

Lesson 10-2: 3-D Views of Solid Figures

Example: Different Views

Front

Left

Right

Back

Top

* Note: The dark lines indicated a break in the surface.

Lesson 10-2: 3-D Views of Solid Figures

Sketch a rectangular solid 7 units long, 4 units wide, and 3 units high using Isometric dot paper .

Sketches

Step 1: Draw the top of a solid 4 by 7 units.

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Lesson 10-2: 3-D Views of Solid Figures

Step 2: Draw segments 3 units down from each vertex (show hidden sides with dotted lines).

Sketches - continued

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Lesson 10-2: 3-D Views of Solid Figures

Step 3: Connect the lower vertices. Shade the top of the figure for depth if desired. You have created a corner view of the solid figure.

Sketches - continued

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Lesson 10-2: 3-D Views of Solid Figures

Imagine cutting a cardboard box along its edges and laying it out flat. The resulting figure is called a net.

back

=

end

end

top

front

bottom

Nets and Surface Area

A net is very helpful in finding the surface area of a solid figure.

Lesson 10-2: 3-D Views of Solid Figures

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Let’s look at another net.

This is a triangular pyramid.

Notice that all sides lay out to be triangles.

Lesson 10-2: 3-D Views of Solid Figures

33

6

6

33

10

10

6

6

6

6

Find the surface area of the figure using a net.
• First, imagine the figure represented as a net.
• Find the area of each face.
• Find the sum of all the individual areas.

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Surface area =

(6 x 10) + (6 x 10) + (6 x 10) + ½(6)(33) + ½ (6)(33) =

60 + 60 + 60 + 93 + 93 = 180 + 183

Lesson 10-2: 3-D Views of Solid Figures