This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series.

In this program we look at applications of area and volume. We do this in the context of three real-world applications. In the first, we look at the sinking of the Titanic in the context of volume and density. In the second application we look at the glass pyramid at the Louvre Museum and calculate its surface area. In the third application we look at the Citibank Tower in New York City to study the ratio of surface area to volume to learn about heat loss in tall buildings.

The sinking of the Titanic provides an opportunity to explore volume, density, and buoyancy. Students construct a mathematical model of the Titanic to determine why it sank and what could have been done to prevent it from sinking.

The sinking of the Titanic provides an opportunity to explore volume, density, and buoyancy. Students construct a mathematical model of the Titanic to determine why it sank and what could have been done to prevent it from sinking.

The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid.

The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss.

This is a collection of definitions related to 3D figures and their properties. This includes definitions and examples of 2D nets of 3D figures, as well as 2D cross-sections of different 3D figures.

This is a collection of definitions related to 3D figures and their properties. This includes definitions and examples of 2D nets of 3D figures, as well as 2D cross-sections of different 3D figures.

This is a collection of definitions related to 3D figures and their properties. This includes definitions and examples of 2D nets of 3D figures, as well as 2D cross-sections of different 3D figures.

The formula for the Surface Area of a Cylinder.

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The formula for the Volume of a Cube.

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The formula for the Volume of a Cylinder.

To see resources related to this topic click on the Related Resources tab above.

The formula for the Volume of a Recantular Prism.

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The formula for the Volume of a Sphere.

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The formula for the Volume of a Square Pyramid.

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Note: The download is a JPG file.

Watch this video to learn about the volume of a pyramid. (The video transcript is also included.)

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Video Transcript

In this activity, learn about the architecture of the Roman Pantheon. This companion to a Google Earth Voyager Story provides a deeper understanding of the geometric concepts introduced in the Voyager Story.

In this Google Earth Voyager Story study the sustainable architecture designed for life in Antarctica. Why Antarctica? There are several research stations in the Antarctic where scientists a great deal of the year conducting research. Also, the Antarctic simulates the harsh climates of planets like Mars, where future explorers will spend years of time in the future. To see the Google Earth version of this lesson go to this link (best viewed in Chrome).

Note: The download is the teacher's guide.

Related Resources

This collection of clip art images includes images of 3D figures and composite figures.