Cross sectional area (NOT A QUESTION)

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Discussion Overview

The discussion revolves around the concept of cross-sectional areas in geometry, specifically how they apply to various three-dimensional shapes such as cylinders, spheres, and ellipsoids. The scope includes technical explanations and clarifications of how to calculate these areas for different geometrical forms.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant explains that a cross-sectional area represents a flat, 2-dimensional view of a 3-dimensional object, using examples like cylinders and spheres.
  • The same participant states that for a cylinder, the cross-sectional area is the area of the base, while for a sphere, it is the area of a circle with the same radius.
  • Another participant humorously acknowledges the previous post without adding further technical content.
  • A different participant mentions that for an oblate ellipsoid, such as Earth, the cross-sectional area can be calculated as pi times the square of the radius.

Areas of Agreement / Disagreement

Participants do not express disagreement on the definitions provided, but the discussion remains informal and lacks depth in technical debate or exploration of competing models.

Contextual Notes

The discussion does not delve into the assumptions or limitations of the definitions provided, nor does it explore the implications of these calculations in practical applications.

Who May Find This Useful

Individuals interested in geometry, particularly those looking for basic explanations of cross-sectional areas in various shapes.

moonman239
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Just for those who don't know a thing about cross sectional areas, I thought I'd explain.

A cross sectional area describes the area of a flat (2-dimensional) representation of a 3-dimensional object. So if I cut a cylinder, instead of seeing two circles, I see four circles (unless there are other circles in my environment). The cross-sectional area is the area of either of the two circles.

For a cylinder or right solid, the cross-sectional area is the area of the base.
For a sphere, the cross sectional area is the area of a circle with the same radius (pi*r2).
For an ellipsoid, the cross sectional area is the area of an ellipse with the same long (a) and short (b) axes (pi*ab).
 
Last edited:
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I don't know what to say. Thanks for sharing?
 
lol at landau's response
 
Oh, for an oblate ellipsoid (such as Earth), where lines of latitude are circular, the area is simply pi*(r^2)
 

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