Architecture
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Volume of sphere tank

ÀÛ¼ºÀÚ Uploader : ezmech ÀÛ¼ºÀÏ Upload Date: 2016-04-04º¯°æÀÏ Update Date: 2016-04-04Á¶È¸¼ö View : 956

Volume of Sphere

Area of circle : A = ¥ð(R^2-(R-h)^2)

Volume(colored)  

For h <= R
V1 = ¥ð¡òR^2-(R-h)^2 dh = 2¥ð¡òR^2-R^2+2Rh-h^2 dh
  = ¥ð¡ò2Rh-h^2 dh = 2¥ð{Rh^2-(1/3)h^3} (from h to 0)
  = (¥ð/3)h^2(3R-h)

For R < h <= 2R
V2 = (4¥ð/3)R^3 - (¥ð/3)(2R-h)^2(R+h)
  = (¥ð/3){4R^3 - (4R^2-4Rh+h^2)(R+h)}
  = (¥ð/3){4R^3 - (4R^3-4R^2h+Rh^2+4R^2h-4Rh^2+h^3)}
  = (¥ð/3){4R^3 - 4R^3 + 3Rh^2 - h^3 }
  = (¥ð/3){3Rh^2 - h^3 }
  = (¥ð/3)h^2(3R-h)

V =  (¥ð/3)h^2(3R-h)


*** Âü°í¹®Çå[References] ***

https://en.wikipedia.org/wiki/Spherical_cap
V = (¥ð/3)*h^(2)*(3*R-h)
º¯¼ö¸í Variable º¯¼ö°ª Value º¯ ¼ö ¼³ ¸í Description of the variable


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