Area of trapezoid formed by slicing a cylinder

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The discussion centers on determining the area of a trapezoid formed when a cylinder of radius R is sliced by a plane at an angle α. Participants explore the geometric implications of the cut, noting that the shape may not be a true trapezoid but rather a truncated ellipse with curved sides. The relationship between the area of the trapezoid and the cylinder's dimensions, including the base area (Abase=π*R²) and the path of magnetic flux, is examined, with suggestions to use integration techniques for accurate area calculation. The ambiguity of the problem is acknowledged, particularly regarding the definition of the trapezoid's dimensions and the projection of the inclined cylinder. Ultimately, the discussion highlights the complexity of visualizing and calculating the area of the resulting shape from the inclined cut.
  • #31
magnetpedro said:
In my opinion it is not. It's a trapezoid because a flux would cross all the length of the cylinder.

Now your talking about the projection of a cylinder into a plane, I believe. The projection would have two parallel sides corresponding to the sides of the cylinder with elliptical end caps. (Whether a projection or a slice at some non-zero angle, you don't get a trapezoid.)

Does the flux pass through the entire cylinder?
 
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  • #32
stedwards said:
Now your talking about the projection of a cylinder into a plane, I believe. The projection would have two parallel sides corresponding to the sides of the cylinder with elliptical end caps. (Whether a projection or a slice at some non-zero angle, you don't get a trapezoid.)

Does the flux pass through the entire cylinder?

Yes, it does!
 
  • #33
Then, I guess you are asking about a projection, which is a long rectangle with the short ends replaced by half an ellipse. If you have a small light source across the room, it's the shadow cast by a soup can near the wall.
 

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