Engaging students: Finding the volume and surface area of pyramids and cones

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Laura Lozano. Her topic, from Geometry: finding the volume and surface area of pyramids and cones.

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C1. How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

Now days, pyramids have appeared almost all over pop culture because of the illuminati conspiracy. Famous artist like Katy Perry, Kanye West, Jay-Z, Beyoncé, and many others are believed to be part of this group that practices certain things to retain their wealth. Since it’s a conspiracy, it might not be true. Although that’s another topic, they all use an equilateral triangle and pyramids to represent they are part of the illuminati group. They display it in their music videos and while they are performing at a concert or awards show.

In Katy Perry’s new music video, were she portrays herself as a Egyptian queen, for some weird reason, she has a pyramid made out of what looks like twinkies.


To make this, the base and height had to be measured to create the surface area of the pyramid.

Also, the picture below is from Kanye West’s concerts. He is at the top of the pyramid.


To make this, they had to consider the size of the stage to fit the pyramid. So the size of the base depended on the size of the stage.

The most famous cone is the ice cream cone. When most people think of cone they initially think ice cream! Ice cream cones are made using the surface area of a cone and taking into consideration the volume of the cone. The bigger the surface area, the bigger the volume, the more ice cream!

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C2. How has this topic appeared in high culture (art, classical music, theatre, etc.)

Some musical instruments have the form of a cone. For example, the tuba, trumpet, and the French horn all have a cone like shape.



The sound that comes out of the instrument depends on the volume of the cone shaped part as well as the other parts of the instrument. The bigger volume of the cone shaped part is, the deeper the sound, the smaller the volume of the cone shaped part is, the higher pitched it is.

Pyramids can be used in art work. Most of the art work done with pyramids is paintings of the Egyptian Pyramids. But, they can also be used to make sculptures of abstract art. Here is one example of an abstract sculpture made from recycled materials.




If the sculpture is hallow, then to make it you would only need the surface area. If it’s not, then you would also need to calculate the volume to see how much recycled material was used.

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D5. How have different cultures throughout time used this topic in their society?

In ancient history, the Egyptians used to build pyramids to build a tomb for pharaohs and their queens to protect their bodies after their death. The pyramids were built to last forever. No one knows exactly how they built the pyramids but people have had theorys on how they were built.

The most famous pyramids are the Pyramids of Giza. The pyramids are Pyramid Khafre, Pyramid Menkaure, and Pyramid Khufu. It is the biggest and greatest pyramid of Egypt. This pyramid used to measure about 481 feet in height and the base length is about 756 feet long. However, because the pyramid is very very old, erosion causes changes in the measurements of the pyramid. When scientiest and archeologist had to find the differrent measurements they most likely used the formula to find the volume and surface area of the pyramid. However, back then, the formula was probably not discovered yet.



An example for cones is the conical hat. Used by most the Asian culture, conical hats, also know as rice hats, or farmers hat, were worn by farmers, and they are still somewhat used today. There are many types of conical hats that can be made today. Some are widder than others, and some are taller than others. To make the hats, the maker of the hat has to consider the surface area of the hat to make the hat properly.







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