Math Project

I thought that maybe it would be a good idea to upload pictures of my calculations on paper. So here are the calculations for all my shapes.

Today I decided to do the calculations for the hexagonal prism. The formula for the volume is  V=bh But we already know the volume. So we can change it to  936.62 cm³ . =bh . The reason this cylinder is different is that we have to choose the size of the base or the height ourselves. I decided to try 2 different options. I started with a height of 30 cm. So I divided  936.62 by 30 and got  31.2206666667.  So that means  31.2206666667 is the area of the base, but to find the surface area we have to figure out the  circumference.  I calculated with the formula 2 square root pi times area, that the circumference is, 19.81. So if you take the height 30  and multiply that with 19.81 you get 594cm  squared. Then you take the area of the circle and them together 31.2206666667+ 594 and  you get  625.220666667. So the surface area is 625.2206666667 cm squared. This is not the most efficient packaging but right now it is  in se...

Today I decided to see if a cube had a more efficient surface area than a rectangular prism. The volume of the cube has to be  936.62 cm³. The formula for the volume of a cube is V=edge cubed. We already know the volume so we can fill in 936.62=edge ³.  So I decided to cube root  936.62. and I got 9.78410585. I decided to check it by cubing it, and I got  936.620000632. Which is almost exactly the same. Now that I have the side length for the cube it is a lot easier to find  the  surface area. The formula for surface area is 6*edge squared. So I squared the edge and got  95.728727284. Then I multiplied  that by 6 and got  574.372363704. So the surface area of the square would be  574.372363704   cm³. Which is less than that of the rectangular prism. So at the moment, it is the most efficient shape. But when I design more shapes later on it may change.  ]

  Today I worked out the volume of my box. Calculations The formula for the volume of a rectangular prism is V=whl.  So in this case width is 4.9 cm, the height is 14.1 cm and the length was 13.6 cm. I multiplied these and I got 936.62  cm³. So the surface area is 654.98 cm squared and the volume is 939.62 cm cubed.  Search Results Web result