Project Description:
Design Your Own Project Write-Up:
In this project we had to chose something to find the volume of. We could have worked independently or with partners. For this project I worked with two other people. We chose to do the One world trade center. For those of you who don't know what that is it is the new world trade center in New York. The first thing that I noticed was that on four of the sides there was a Pyramid cut out. Also that on the bottom there was concrete cube to help against attacks on the building. To start the math we had to get the dimensions of the building. They were a 200ft x 200ft base that was 1776 ft tall. At the bottom there is a 200ft x 200ft x 186ft concrete base to help protect against and attacks that could come onto the building itself. So to get that volume we would just multiply them all together. That would give you 7,440,000 ft^3. Now we need to know how tall the building is from that point. To do that we would subtract 186 from 1776. That would give you 1590. Now if we look at the image you can see that on 4 sides there are pyramids that go into the building. So next we need to find out how far they go into the building. To do that we need to know what the dimensions are for the top part of the building. To do that we can use the Pythagorean theorem. To get the side lengths if we look at the square at the top we can see that it is at a 45 degree angle to the one at the bottom. So we can say that from one edge to the opposite one it is the original side length of 200. So if we half that to get 100 we have a triangle with side length of 100ft x 100ft x an unknown hypotenuse. So now if we use the Pythagorean theorem we can do 100^2 x 100^2 to get us our hypotenuse. After that we need to square root that answer. That would get you ~140. Now that we know that we can say that the triangle go in 60ft. So by knowing that we can say that the triangles go in 30ft. So we can now find the volume of one of those pyramids. To do that we would have to half the side length of 140 to get 70 because it is a triangle at the top. Then we would multiply 70 x 30 x 1590 our height. Then we would need to divide by 3 because it is a pyramid. That would give you 1,113,000 ft^3. So next we need to take the building and turn it into a normal rectangular prism. To do that you need to take 200 x 200 x 1560. That you give you 63,600,000. Now you need to subtract the 4 pyramids. To do that you will need to take the number we got earlier, 1,113,000 and multiply it by 4 to get 4,452,000. Then subtract that number from the rectangular prism and you will get 59,148,000ft^3. Now you need to add the concrete base on the bottom. Once you do that you will get 66,588,000ft^3. That is how we got the volume of the one world trade center.
Project Reflection:
For this project I had to use the habit of a mathematician to stay organised. I had to do that because if I didn't the math that I was doing would have gotten very messy. I also had to use the Habit to take apart and put back together. If I did not do that What I was doing would have been a lot harder to do. An example of that was when I took off the concrete block at the bottom of the building. I think that this project was a very long one. I think that because it was so long we had forgotten what we did at the beginning. I also thought that a lot of what we did during this project especially during the beginning of the project was review. As we got farther into the project we did do some challenging things. Although I think that we spent a lot more time on one subject then we had to I think it was needed for the people who didn't understand the subject as well as I did. Although I believe that their should have been the option for those who understood the subjects better to move along faster than the others. I do think that this project was mostly a waste of time but, we did learn some new things. Those things that I learned I do know that I can use them outside of High School.
Design Your Own Project Write-Up:
In this project we had to chose something to find the volume of. We could have worked independently or with partners. For this project I worked with two other people. We chose to do the One world trade center. For those of you who don't know what that is it is the new world trade center in New York. The first thing that I noticed was that on four of the sides there was a Pyramid cut out. Also that on the bottom there was concrete cube to help against attacks on the building. To start the math we had to get the dimensions of the building. They were a 200ft x 200ft base that was 1776 ft tall. At the bottom there is a 200ft x 200ft x 186ft concrete base to help protect against and attacks that could come onto the building itself. So to get that volume we would just multiply them all together. That would give you 7,440,000 ft^3. Now we need to know how tall the building is from that point. To do that we would subtract 186 from 1776. That would give you 1590. Now if we look at the image you can see that on 4 sides there are pyramids that go into the building. So next we need to find out how far they go into the building. To do that we need to know what the dimensions are for the top part of the building. To do that we can use the Pythagorean theorem. To get the side lengths if we look at the square at the top we can see that it is at a 45 degree angle to the one at the bottom. So we can say that from one edge to the opposite one it is the original side length of 200. So if we half that to get 100 we have a triangle with side length of 100ft x 100ft x an unknown hypotenuse. So now if we use the Pythagorean theorem we can do 100^2 x 100^2 to get us our hypotenuse. After that we need to square root that answer. That would get you ~140. Now that we know that we can say that the triangle go in 60ft. So by knowing that we can say that the triangles go in 30ft. So we can now find the volume of one of those pyramids. To do that we would have to half the side length of 140 to get 70 because it is a triangle at the top. Then we would multiply 70 x 30 x 1590 our height. Then we would need to divide by 3 because it is a pyramid. That would give you 1,113,000 ft^3. So next we need to take the building and turn it into a normal rectangular prism. To do that you need to take 200 x 200 x 1560. That you give you 63,600,000. Now you need to subtract the 4 pyramids. To do that you will need to take the number we got earlier, 1,113,000 and multiply it by 4 to get 4,452,000. Then subtract that number from the rectangular prism and you will get 59,148,000ft^3. Now you need to add the concrete base on the bottom. Once you do that you will get 66,588,000ft^3. That is how we got the volume of the one world trade center.
Project Reflection:
For this project I had to use the habit of a mathematician to stay organised. I had to do that because if I didn't the math that I was doing would have gotten very messy. I also had to use the Habit to take apart and put back together. If I did not do that What I was doing would have been a lot harder to do. An example of that was when I took off the concrete block at the bottom of the building. I think that this project was a very long one. I think that because it was so long we had forgotten what we did at the beginning. I also thought that a lot of what we did during this project especially during the beginning of the project was review. As we got farther into the project we did do some challenging things. Although I think that we spent a lot more time on one subject then we had to I think it was needed for the people who didn't understand the subject as well as I did. Although I believe that their should have been the option for those who understood the subjects better to move along faster than the others. I do think that this project was mostly a waste of time but, we did learn some new things. Those things that I learned I do know that I can use them outside of High School.