In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume.

All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism.

In this video, students see a derivation of the formula for the volume of a pyramid. This involves a hands-on activity using unit cubes, along with analysis, and a detailed algebraic derivation.

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.

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.

The formula for the Volume of a Cube.

The formula for the Volume of a Cylinder.

The formula for the Volume of a Recantular Prism.

The formula for the Volume of a Sphere.

The formula for the Volume of a Square Pyramid.

Note: The download is a JPG file.

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

In this Google Earth Voyager Story learn about the geometric concepts that underly sustainable architecture. How do architects build tall skyscraper that can retain heat when its cold?

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.

In this Google Earth Voyager story visit pyramids around the world and learn about the geometry of pyramids. In this lesson, visit the pyramids of Giza and learn about the properties of pyramids. In particular, see the derivation of the formula for the volume of a pyramid.

In this Google Earth Voyager story visit pyramids around the world and learn about the geometry of pyramids.