Math: Pyramids Assignment - Investigating & Application

Pyramids Investigation & Application Assignment

In this assignment, we basically looked at different parts of a pyramid. Especially the slant height on their sides. We were given the formula on how to find the slant height of a pyramid when given the base and vertical height of a pyramid. We were then to find out how the equation works. The Pythagorean theorem is applied into the formula basically. Then, we looked at some Aztec Pyramids (ones with a flat top) and equations on finding the slant height of an Aztec Pyramid. This time we were asked to explain how the equation works. It also uses the Pythagorean theorem and also the properties of trapezoids. Then, we were asked to apply our knowledge of these equations to find different measurements with the other measurements of a true pyramid. Then, we were asked to make a net for a pyramid only provided with the base and the vertical height of it. In this assignment, I did pretty well - 7/8 for investigation and 7+/8 for Application.

Science One World Investigation Project

Science Solar Cooker

For this project, we had to use our knowledge about refraction, reflection, and some previous knowledge of insulation to make a device that can heat up food using the heat from the sun, with portability, serving the purpose of cooking food in areas that lost or do not have access to fire or electricity.

For this project, I went with a small solar cooker at first. I chose that because I wanted it to be portable, and I thought that a smaller space would allow the radiation to be more focused (trapped and condensed) in the container. It turns out it couldn't collect enough energy with that small area. Moreover, there was a failure of using reflection to aim to a hole into the container. Also, I added too many layers that were suppose to absorb heat and keep the heat in, but all it did was keep the heat out. After the first trial, I left it at school so I had to create a new one and conduct more trials.

First solar cooker design

The second design I came up with was a transparent one. It has a built-in thermometer so the temperature could be observed easily. It was also transparent so heat / infrared radiation can come in from any angle. The design was simple and easy to use. The magnifying glass serves as a transparent cover but also focuses heat into one spot. I made some improvements and finally covered a tissue box with aluminium foil so there is a bigger are that collects the radiation. The aluminium foil also prevents radiation going in, out of the plastic bottle and away, but reflects it back in the bottle again.

These ideas were based on my knowledge, and the idea of the tissue box is from other solar ovens. I tried to not do the same as all the others I have found. I tried to be different. The second design was much better than the first one. The results were about 10ºC every 15 minutes. But what I heard of my classmates' was much higher. So next time, before getting too confident, I would consider why everyone else on the internet uses the same design and find out the reason behind it. However, it was a fun and great learning experience.

My lab report:

https://docs.google.com/a/huskymail.cis.edu.sg/document/d/1cAgRIMCxfqDhfQnJLIvtzPvb_1EenaHnTV565eDYBjA/edit?usp=sharing

Investigation - The Circumference of a Circle

As you may be able to guess from the title, this investigation is about the circumference of a circle. We are trying to find how many times a diameter of a circle can go into the circumference of a circle. Although some of us already know that before, we are asked to prove if it is correct. And it is of course 3.14 times.

The first task was to get a chalk and tie it to a string about one metre and something long. Then, we measure it and cut it to a meter (recommended to do so when stretched). Then, we draw a circle on the ground and that would make the diameter 2 metres as the radius is 1. However, we have to very careful to not pull the string or pull the string when drawing the circle, depending if the string's cut stretched or not. And then, we have to take out the chalk, cut the string into a metre when not stretched, and then lay it on the circumference perfectly and see how many times it can fit in the circumference. The string would fit in about 6 times as it's the length of the radius, which means the diameter goes into the circumference about 3 times. Technically, it should be 22/7 or at least 3.14, but approximately it is 3 times. (I do think it would be more precise and straightforward if we make the diameter a multiple of 7, and find out if the circumference is the multiple of 22. That would prove it too.)

Then, we did some exercises dividing the circumference by the diameter and finding out if it's around 3.14. Of course, again, technically it should be 22/7, but approximately it is 3.1 times. That's because the measurements are to the nearest tenth.

I had no difficulties and I have figured out the solution quickly before taking the task. I totally understand it also. However, I didn't use any diagrams. We did discuss the purpose of this investigation and the discussed that π is 22/7 with the proof from the numbers we found out in the investigation.