Measuring Your World
Project Description
In this project, we were assigned the task of measuring the volume of an any object of our choice. What I decided to measure was a keyboard piano stand. The reason that I chose to measure a keyboard stand was because of the different cylindrical and rectangular prisms of the stand. Cylindrical and rectangular prisms have been something I have been familiar with for quite some time now, I knew measuring this would be within the realm of something I knew how to do. The formula I used to calculate the cylinders was π(Radius x Radius)Height, which finds the area of the base of the cylinder and multiplies it by the height. In a way created a stack of one-dimensional circles. To find the volume of the rectangular prisms, I used the formula Height x Width x Length. This formula is similar to the cylinder's formula for volume, because of the way it stacks the one-dimensional rectangles into a two-dimensional object. And so, with the knowledge of the formulas, I began my work.
Process & Solution
➕➗-
➕➗-
1. Measurement and Data
I began this project by first sketching out a complete drawing of the keyboard stand and sketching out all of the separate three dimensional prisms that make up the entire keyboard stand. Once I had my sketches of the keyboard stand and all of it's cylindrical and cuboid parts, I took the measurements of all of the specific edges and lines to find the dimensions of the specific prisms that make up the keyboard stand. As I took the measurements of the each line and edge, I labeled each of the specific prisms with their dimensions. (This specific work shown to the bottom left.)
I began this project by first sketching out a complete drawing of the keyboard stand and sketching out all of the separate three dimensional prisms that make up the entire keyboard stand. Once I had my sketches of the keyboard stand and all of it's cylindrical and cuboid parts, I took the measurements of all of the specific edges and lines to find the dimensions of the specific prisms that make up the keyboard stand. As I took the measurements of the each line and edge, I labeled each of the specific prisms with their dimensions. (This specific work shown to the bottom left.)
2. Calculating Specific Volume
After finding all of the dimensions for the prisms, I first calculated the volume of all of the cylindrical prisms on the keyboard stand. (As you can see to the tope right.) I calculated the volume using formula:
After finding all of the dimensions for the prisms, I first calculated the volume of all of the cylindrical prisms on the keyboard stand. (As you can see to the tope right.) I calculated the volume using formula:
V= (π)(Radius × Radius)(Height)
Once I had found the volumes of all the cylindrical three dimensional shapes, I calculated the volume of the rectangular prisms. Using the Formula:
Volume= Length × Width × Height
Both of these formulas work to find the volume of the different prisms because they both first calculate the area of the prisms' two identical bases and multiply that times the height, which in a way calculates how many shapes are lined up to create the prism.
Volume= Length × Width × Height
Both of these formulas work to find the volume of the different prisms because they both first calculate the area of the prisms' two identical bases and multiply that times the height, which in a way calculates how many shapes are lined up to create the prism.
3. Adding It All Together
I had all of the necessary volumes of the prisms that I needed, all I needed to do was add the volumes together to find the true volume of the entire keyboard stand. The work that I did leading up to this and solution to the problem you are able to see on the bottom of the page above. Once I had added all of the volumes together the solution to the problem was: 1,991.73 cubic centimeters
I had all of the necessary volumes of the prisms that I needed, all I needed to do was add the volumes together to find the true volume of the entire keyboard stand. The work that I did leading up to this and solution to the problem you are able to see on the bottom of the page above. Once I had added all of the volumes together the solution to the problem was: 1,991.73 cubic centimeters
Summary of Mathematical Concepts
What went into finding a solution to the problem for the entire object was quite a process. The mathematical concepts and processes that went into the project included measurement, visualization, the arithmetic, application of formulas, addition, leading ultimately up to the solution. Measurement, an easy concept to comprehend, was time taken to measure the necessary edges and lines of the object, collecting the essential data to continue into the arithmetic. Once the data was found, the visual of the object’s counterparts were created to show the different types of prisms within the entire object. The problem solving and arithmetic of this project involved applying the data that I had collected into the specific formulas to find the volumes. The visualization of the object’s counterparts would then be applied by finding out what specific formula would need to be used to find the specific counterpart. When the objects counterparts had each of their own volumes, all of those volumes would be added together creating the solution. In this case, the solution would be the volume of the entire keyboard stand.
Reflection
This project was fun for me because I felt like I could apply my knowledge of the different formulas to a real life situation. But at the same time I didn't feel that challenged by the math itself. The most challenged I felt was by the organization of the data because there were a lot of different measurements that I had to record and different edges and lines that I had to label. My organization skills were definitely put to the test during this project, collecting all of the data. Another skill (Habit of a Mathematician) that I had to utilize was knowing how to break down the problem and start small. In order to have measured the volume of the entire keyboard stand was by literally breaking it down on paper. I had to begin by first measuring the stand's counterparts and proceeding from there. After having all of the object's counterparts I was able to look at the object as whole and add all of the volumes together. Therefore by starting small I was able to ultimately solve the probably as a whole.