For this project we chose to measure a soccer ball because there were many different ways we could break it down and all my group members are interested in soccer. We measured it using 3 rulers, two on the sides perpendicular to the ground, and 1 on top parallel to the ground. We found that the radius was three. Then we counted the number of pentagons on the soccer ball and there were 12. Each side of a pentagon was 2.125 inches.
You can see all our calculations in We divided up a pentagon into 5 equal isosceles triangles so we could find the area of one of them. Then we split that triangle in half down the middle to make a right triangle. We knew the angles of that triangle since 360/5 is 72 and half of that is 36. We then used our trigonometry functions to find the height of the triangle which was 1.4624 inches. Then we used the area formula (bh/2) to find the area of that triangle using 2.125 as the base. That gave us 3.1076 which we divided by two and got 1.5538. Finally we multiplied it by 5 since there were 5 of those triangles in one pentagon and got 7.769. After that we had to find the volume of one of the pyramids with a pentagon base since soccer balls are made of a bunch of different pyramids that converge in the very center of the ball. It was pretty simple, though, since we already had the area of the base. The formula is lwh/3 or ah/3 since l times w equals the area. So we took our area multiplied it by three (height) and divided it by 3 (part of the formula). It turned out the volume was the same as the area since the height was three but they were in different units. Square inches compared to cubic inches. Lastly we just multiplied the volume by 12 since there were 12 different pentagons on the ball to get a total volume of 93. 228. Overall I really enjoyed doing this project and I learned a lot throughout it. One challenge we faced was bringing in the materials because we kept forgetting to bring them which stalled our progress a little. We overcame it, though, and brought in the materials so we could have a successful project. We decided the roles at the beginning so everyone knew what they had to get done. That way we could get right to work and didn't waste any time figuring out the logistics of it. I would not do anything differently if I could. I thought we were really efficient and did a good job. Two habits of a mathematician we used were Take Apart and Put Back Together and Describe and Articulate. The first one was used because we took apart our item into smaller pieces to make it easier to calculate. Then we just multiplied it to get it back to its original shape. We used the second habit a lot. First when we were sharing our thinking and our ideas I drew it out mine to make it easier to understand for my group mates. That really helped them grasp what I was trying to say. We also used it when we had to present in front of our class. We took our work, which we had drawn out, and used it to describe our thinking and reasoning behind our solution. |