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.

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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.

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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.

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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.

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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. Students look at different graphs of these functions for different organisms. 

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This is the transcript for the video of same title. Video contents: 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. Students look at different graphs of these functions for different organisms.

To view the full video: https://www.media4math.com/library/algebra-applications-rational-functions-segment-2-biology

A Promethean Flipchart is available for this video: https://www.media4math.com/library/promethean-flipchart-algebra-applications-biology

This is the transcript for the video of same title. Video contents: 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.

To access the full video: https://media4math.com/library/geometry-applications-area-and-volume

Surface Area: Example 6. Find the Surface Area of a triangular prism when all measurements are expressed as variables.

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Surface Area: Example 22. Find the Surface Area of a hollow cube when all measurements are expressed as variables.

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Surface Area: Example 7. Find the Surface Area of a hollow triangular prism when all measurements are expressed as numbers.

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Surface Area: Example 23. Find the Surface Area of a cone when all measurements are expressed as numbers.

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Surface Area: Example 8. Find the Surface Area of a hollow triangular prism when all measurements are expressed as variables.

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Surface Area: Example 24. Find the Surface Area of a cone when all measurements are expressed as variables.

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Surface Area: Example 9. Find the Surface Area of a cylinder when all measurements are expressed as numbers.

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Surface Area: Example 10. Find the Surface Area of a cylinder when all measurements are expressed as variables.

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Surface Area: Example 11. Find the Surface Area of a hollow cylinder when all measurements are expressed as numbers.

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Surface Area: Example 12. Find the Surface Area of a hollow cylinder when all measurements are expressed as variables.

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Surface Area: Example 13. Find the Surface Area of a pyramid when all measurements are expressed as numbers.

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Surface Area: Example 14. Find the Surface Area of a pyramid when all measurements are expressed as variables.

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Surface Area: Example 15. Find the Surface Area of a truncated pyramid when all measurements are expressed as numbers.

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Surface Area: Example 16. Find the Surface Area of a truncated pyramid when all measurements are expressed as variables.

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Surface Area: Example 1. Find the Surface Area of a rectangular prism when all measurements are expressed as numbers.

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Surface Area: Example 17. Find the Surface Area of a sphere when all measurements are expressed as numbers.

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Surface Area: Example 2. Find the Surface Area of a rectangular prism when all measurements are expressed as variables.

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Surface Area: Example 18. Find the Surface Area of a sphere when all measurements are expressed as variables.

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