Geometry has taken over our grade eight math classroom! We took the inside of our classroom door and made it five times bigger, using shapes and our creativity. Our teacher covered it in a white piece of paper and split it up into five sections. Each of our groups got a section, then from there we had to figure out how we would cover the space in shapes to make the overall surface area five times bigger.
Just The Beginning
In the beginning of the project my group was so confused! But we took all of our ideas and tried them out, eliminating the ones that didn’t quite work. As we went along we bumped into many problems, but we keep working them out as a group. At one point near the end, we realized that our door was going to be to small and under five times bigger. That was when we got creative.
In the picture above it shows what we had before we realized that we could do anything we wanted to make the surface area bigger. So we got creative and realized that when you put the shapes on the door, whatever side is facing down, the area of that side gets taken away. So we thought maybe you could put the base side of the rectangles we wanted to add to our door on the tips of the square pyramids? That way it wouldn’t take away any surface area.
Thats what we did, and it worked! It also added some creativity to our door and showed that we worked afraid to think outside the box.
The Classes Finished Door!
In the end of our project we had to write out a Technical Report where we answered some questions about our overall project, team work abilities, showed and explained all of our formulas and how we got our outcome.
This Is Our Technical Report
The objective of our project was to create the surface area of our classroom door five times bigger. However while we were working we realized that the project was also so we could learn how to apply the mathematics we learn in the classroom to the real world. This door project was based on engineering and we used our math skills to help us find the solution.
The roles and responsibilities within our group were fairly equal. Lucy and Taylor did most of the math calculations, however our group members made sure everyone understood the math and participated at something in each area. Aedan and Kyle were a big help with the drawing, cutting, assembling and taping of the shapes.
Our group would all agree that we were working in a bad group dynamic at the beginning, know one could decide on a plan and everyone was confused. We all eventually realized, and started considering our group members strengths and weaknesses so we could help each other a little more. The project got more and more fun over time but working together is a lot easier and makes everything more fun. By the end of the project we all agreed that we’re happy with the project we completed.
Our percentage error was about 0.02% over the amount wanted. This was because a couple of the shapes had side lengths that were 0.04 cm too short. The area we needed was 17228.25 cm squared. We ended up having 17231.54 cm squared.
Area Of Our Door Section: 3445.65 cm squared
Area We Wanted To Get To: 17228.25 cm squared
Rectangle
Area Of One Rectangle: 547.6 cm squared
Height: 14.8 cm
Width: 7.4 cm
Area Of All Three Rectangles: 2190.4 cm squared
Square
Area: 245.76 cm squared
Hight: 6.4 cm
Width: 6.4
We originally wanted to make four rectangles to put on the left over space from the cylinder which was 433.3 cm. After figuring out that we would of gone around 200 cm over the surface area we wanted on the door, our group decided to make three rectangles with an area of 547.6 cm squared. Once we did this we created one more shape to fill up our door completely, a square. The squares dimensions were a hight and width of 6.4 cm and an area of 245.76 cm squared.
Square Pyramid
Smaller Square Pyramids
Area Of all Triangles: 324.8 cm squared
Hight: 20.15 cm
Area: 81.2 cm squared
Length/ Width : 8.06 cm
Area Of Bases: 64.96 cm squared
Bigger Square Pyramids
Base length/ width: 13.4 cm
Area of base: 179.56 cm squared
Hight of triangles: 33.5 cm
Area of all triangles: 897.8 cm squared
Ratio of both square pyramids width to hight: (1:25)
We decided to make a square pyramid and make the triangles five times bigger that the base. We found the pyramid base had a length of 7.6 cm and a hight of 20.15 cm. The area of the triangles 288.8 cm squared and the area of the bases was 57.76 cm squared. To make it to scale we found how much taller the hight had to be than the base.
We took the length of our section of the door and divided it by 5. This was our width and we multiplied it by 2.5 to get our hight. We made five pyramids with these dimensions on one row they were the smaller square pyramids on our door. Then we divided the length of the door by 3 to make twelve bigger pyramids sitting three per row.
We took the length of three pyramids, 13.43 cm and multiplied it by 2.5 to get the hight of 33.6 cm. We made twelve of these pyramids in four rows.
The remaining hight was 22 cm so the remaining space to cover was 886.6 cm squared.
Cylinder
We decided to make a cylinder with a base that was one quarter the space we had left. We wanted the rest of the cylinder to be nine times the area of the base so it would cover for half of the remaining space.
Hight: 37.5 cm
Diameter: 16.8 cm
Area Of Base: 221.65 cm squared
Circumference: 52.8 cm
Area: 2,422.55 cm squared
Area Without Base: 2,201.65 cm squared
Conclusion
Pyramids Area: 1624 cm squared (small pyramids) 10773.6 cm squared (big pyramids)
Cylinder Area: 2201.65 cm squared
Rectangular Prism Area: 2190.4 cm squared
Cube Area: 245.76 cm squared
Leftover Area: 664.95 cm squared
Project By: Taylor, Aedan, Lucy and Kyle
BYE 🐳