Description.
The Measure your world project was focused on learning the different parts of life that use measurements. The point of this project was to relate the formulas that we learned in class to the real world. This was a long journey, but through it we learned that the everyday objects around us have a part in the math world. This process started with re-introducing the Pythagorean Theorem. We learned about this theorem in 9th grade, but most of us forgot it’s purpose. We used the Pythagorean Theorem to derive the distance formula. Which we used to help us find the equation of a circle (x^2+y^2=1). Through these different formulas and equations we began to understand how right triangles are important to trigonometry. Once we were well versed in the review, we started to incorporate new information. This include sine, cosine, & tangent. They are the functions of a right triangle. We learned that theta represents an angle. Before we start to use these equations we have to find our theta. This is the angle we are trying to solve for. We have to choose the function that will help us solve for that angle. We use the angles we already have to plug into the three equations we have. The first is sine. Sine = The opposite line farthest away from theta / The hypotenuse of the line. Cosine = The line adjacent line of theta / The hypotenuse of the line. Tangent = Opposite line / Adjacent. These are the main functions of right triangle trigonometry. We can use this knowledge to take apart different shapes that have triangles within them to solve then put back together. This moved to use learning how to solve for the area of a circle using the formula Area= π *radius^2. We began to look into different shapes and their formulas. This was the start of our project. I decided to measure a mug.
Write-Up.
For this project it was our job to find the volume of a shape that is in our everyday lives. This project was made so we can relate how math is in everything around us. Hence the name “Measuring Your World”. I started with project in a group who was measuring something that I wasn’t very interested in. This was the first project in math that I decided to work alone in and I truly believe it was for the best. I wanted to measure something that I was excited about, and I ended up choosing to measure the volume of clay used in my teacher's mug. This happened because before I came to show my project idea to my teacher I simply wanted to measure the volume of the mug. He challenged me to measure the amount of clay used to make the mug. This would mean I would have to measure the outside and inside volume of the mug, then include the base volume.
Math.
Outer Height: 6.25 Inches
Outer Circumference: 16.75
Inner Height: 5.75 Inches
Inner Circumference:15 Inches
To solve for volume I have to have the Radius, so I plugged in my circumference to the radius formula.
r=c/2 π
Outer Radius:
r=16.75/2 π
r=2.67
Inner Radius:
r=15/2 π
r=2.39
Now that I have all my measurements I can plug them into the right cylinder formula.
Outer Volume
V=π 2.67^2*6.2
V=139.98
Inner Volume
V=Π 2.39^2*5.75
V=103.18
To find the amount of clay used I have to subtract the outer volume from the inner volume.
139.98-103.18=36.8
Now I have to add the bass, which is also a right circumference.
Diameter is 4.75
Radius is 4.75/2=2.375
Height is .125
V=π r2t
V=π*2.375^2*.125
V=2.375^2*.125
V=5.65*.125
V=.71*π
V= 2.22
When we add the base our total volume is 39.09 Cubic Inches. Piecing together all of these parts was a very interesting journey. There was time where it was very difficult, but there were times when everything fit perfectly. I truly feel that this was my favorite project in math so far.
Outer Circumference: 16.75
Inner Height: 5.75 Inches
Inner Circumference:15 Inches
To solve for volume I have to have the Radius, so I plugged in my circumference to the radius formula.
r=c/2 π
Outer Radius:
r=16.75/2 π
r=2.67
Inner Radius:
r=15/2 π
r=2.39
Now that I have all my measurements I can plug them into the right cylinder formula.
Outer Volume
V=π 2.67^2*6.2
V=139.98
Inner Volume
V=Π 2.39^2*5.75
V=103.18
To find the amount of clay used I have to subtract the outer volume from the inner volume.
139.98-103.18=36.8
Now I have to add the bass, which is also a right circumference.
Diameter is 4.75
Radius is 4.75/2=2.375
Height is .125
V=π r2t
V=π*2.375^2*.125
V=2.375^2*.125
V=5.65*.125
V=.71*π
V= 2.22
When we add the base our total volume is 39.09 Cubic Inches. Piecing together all of these parts was a very interesting journey. There was time where it was very difficult, but there were times when everything fit perfectly. I truly feel that this was my favorite project in math so far.
Reflection.
This project started as something very different than how it ended. It started with me being uncomfortable with the ideas that my group members had for our final product. Then to me branching out and solving these problems by myself. I’ve noticed that a lot of my greatest accomplishments in math start with a not so happy beginning. During the duration of this project the two habits of a mathematician that I followed was being systematic and making conjectures. I really wanted to make my presentation very easy to follow and for my steps to be clear. The steps I followed to get there was when I was doing my math, I made sure I had it all organized and labeled. This made finishing my presentation very easy. While I was working on some parts of the math I would get tripped up on certain equations. I would have moments of not know if I should multiply or divide, but being the Aries that I am I wouldn’t just wait for class I would test them and see if the results worked. I learned that trying to get the answers on your own is fine, but always get it checked if you think there might be something wrong. I definitely enjoyed doing this project and forming a connection with a mug. I hope that I can take what I learned and apply it to my work in the projects to come.