First, the research content:
1. How to cut a square cardboard into a cuboid carton without a lid?
2. How to cut the paper box to maximize it?
Second, research methods:
Practice, drawing, tabulating, calculating and observing.
Third, the research process:
1. Through observation, I found that we can deduce how to cut a square cardboard into a cuboid carton without a cover by the expansion diagram of the cube.
According to the question, the length of the rectangle =20cm.
Suppose the side length of the square is cut off =X, and the area of the rectangular carton without cover = v.
Cut off the area of a rectangular box with square sides and a long cuboid.
When X= 1, V=324 cm2.
When X=2, V=5 12 cm2.
When X=3, V=588 cm2.
When X=4, V=576 cm2.
When X=5, V=500 cm2.
When X=6, V=384 cm2.
When X=7, V=252 cm2.
When X=8, V= 128 cm2.
When X=9, V=36 cm2.
As can be seen from the figure, the formula for calculating the volume of this box should be: v = (20-2x) 2x,
It is known that when X=3, the cuboid carton has the largest volume.
So is it the biggest? Is the maximum value between 2 and 3 or between 3 and 4?
When X=2.9, V=584.756.
When X=3. 1, V=590.364.
It can be concluded that the maximum volume of rectangular cartons is between 3 and 4.
Cut off the area of a rectangular box with square sides and a long cuboid.
When X=3.2, v = 591.872cm2.
When X=3.3, v = 592.548cm2.
When X=3.4, V = 592.45438+06cm2.
When X=3.5, V=59 1.500cm2.
V=589.824cm2 when X=3.6.
When X=3.7, V=587.4 12cm2.
When X=3.8, v = 584.288cm2.
When X=3.9, v = 580.476cm2.
As can be seen from the figure, when x is between 3 and 4, 3.3 is the maximum value.
Harvest and reflection:
I benefited a lot from writing this research report, because it increased my knowledge of mathematics and computers. Writing this research report also cultivated my spirit of studying hard. But because it's the first time, I can't be perfect, and there must be some shortcomings, but I believe I will write my second and third times better and better through later study.