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 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 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 Surface Area of a Cube.

The formula for the Surface Area of a Cylinder.

The formula for the Surface Area of a Rectangular Prism.

The formula for the Surface Area of a Sphere.

The formula for the Surface Area of a Square Pyramid.

The formula for the Surface Area of a Triangular Prism.

The formula for the Surface Area of a Triangular Pyramid.

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?

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.

This is part of a collection of math examples that show how to area and perimeter for different geometric shapes.