Surface area Definition and 25 Discussions

The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.
A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.

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  1. brotherbobby

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    Problem statement : I draw the problem statement above. I hope I am correct in inferring that the bowl is hemispherical. Attempt : I could not attempt to the solve the problem. We are given that the rate of change (decrease) in volume is proportional to the surface area ...
  2. A

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  3. E

    B How to determine force based on pressure

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  4. Adesh

    I Why volume is conserved but not the surface area?

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    • Adesh
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    • fluid mechanics surface area surface tension volume
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  5. A

    B Surface area problem -- Area of the circle enclosed by the current produced by an electron in a hydrogen atom

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  6. S

    I Strain of of a bubble's surface interface during vibrations

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  7. JD_PM

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  8. JD_PM

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  9. gasar8

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  10. J

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  11. Anachronist

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  12. T

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  13. A

    B How to find the appropriate area in Gauss' law

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  14. adsorption

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  15. D

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  16. Oannes

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  17. Thales Costa

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  18. B

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  19. T

    Silly theoretical area question

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  20. S

    Minimizing surface area of a shaker

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    • SpanInq
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  21. alphaj

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  22. J

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  23. K

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  24. I

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  25. O

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