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Wie groß müssen Radius und Höhe sein, damit die Oberfläche minimal ist?

Approach

´S(r) = 2 pi r^2 + 2V/r´

´S'(r) = 4 pi r + (2V/r)'´ ´S'(r) = 4 pi r + 2V(1/r)'´ ´S'(r) = 4 pi r + 2V(-1/r^2)´ ´S'(r) = 4 pi r - (2V)/r^2´

Nullstellen:

´r = 1/(root 3 (10^9 2 pi)) m = 0.054 cm´

´h = (1 cm^3)/(r^2 pi) ~~ 108.2 cm´


Solution

  • ´r = 0.054 cm´

    ´h ~~ 108.2 cm´

  • URL:
  • Language:
  • Subjects: math
  • Type: Calculate
  • Duration: 25min
  • Credits: 3
  • Difficulty: 0.5
  • Tags: hpi optimization
  • Note:
    HPI, 2014-05-12, Mathe 2, Aufgabe 23
  • Created By: adius
  • Created At:
    2014-07-26 13:43:43 UTC
  • Last Modified:
    2014-07-26 13:43:43 UTC