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Cylinders and Scale
Today, we had for materials a film canister, a white sheet of paper, a sheet of graph paper, a ruler and scissors.
The first thing that we had to do was to find the correct measurements of the canister by using the white sheet.
By rolling up the sheet of blank paper inside the canister, then cutting it to the right dimension and unrolling it, we obtained a rectangle which we measured. We then could confirm that the circumference measured 10 cm and the height 5 cm.
The surface area of the cylinder was thus equal to 10 X 5 = 50 cm.
We then used a stiff sheet of paper. We cut out a rectangle whose dimensions were the double of dimensions of the first rectangle.
The length was thus 10 X 2 = 20 cm and the width 5 X 2 = 10 cm. We calculated the surface of this rectangle using the formula: With = L X L. This surface was thus of 20 X 10 = 200 cm2.
Then we tripled the dimensions of the first rectangle and we obtained a surface of 30 X 15 = 450 cm2. Then quadrupled dimensions of the first rectangle and we obtained a surface of 40 X 20 = 800 cm2 . It was then that we understood! We then could fill out the following tables:
Cylinders Chart
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COEFFICIENT
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HEIGHT
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CIRCUMFERENCE
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DIAMETER
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SIDE SURFACE
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VOLUME
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1
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5cm
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10cm
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3.3cm
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50cm
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1 unit
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Table of proportionality:
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Coefficient
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Height of
Cylinder
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Circumference
of base
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Diameter of
base
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Area of Cylinder
Surface
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Volume
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1
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1
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1
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1
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1
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1
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2
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2
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2
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2
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4
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8
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3
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3
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3
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3
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9
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27
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4
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4
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4
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4
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14
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16
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5
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5
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5
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5
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25
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125
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By taking into account the proportionalities above, we realized that instead of working on the dimensions of a rectangle, we were working on the dimensions of a cube.
Summary: We worked on dimensions of a rectangle. For that we varied two dimensions: the length and the width. For the cylinder, L = H (height) and L = © (circumference). Then to measure the diameter, we varied three dimensions.
example:
This is a tower by the architect Aillaud, located in the town of Nanterre (Top of the Seine). They are juxtaposed cylinders, with clouds that are painted on a blue background. They are classified as an historic building. The Aillaud towers prove to us that we can make fantastic assemblies with cylinders.
