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# Bodies with fixed volume and minimal surface

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Bodies with fixed volume and minimal surface

Author: Valery Ochkov (http://twt.mpei.ac.ru/ochkov/v_ochkov.htm)

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1. Cylinder with a bottom

Volume (V)

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 (1.1)

Surface (S as function of V and d)

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 (1.2)
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 (1.3)

A = d / h if S is minimal

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 (1.4)

2. Cylinder with a bottom (see above) and a cover

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 (2.1)

Surface (S as function of V and d)

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 (2.2)
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 (2.3)

A = d / h if S is minimal

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 (2.4)

3. Cylinder with a bottom and one central vertical dividing wall

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 (3.1)
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 (3.2)
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 (3.3)
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 (3.4)
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 (3.5)

4. Cone

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 (4.1)
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 (4.2)
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 (4.3)
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 (4.4)
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 (4.5)

5. Cone with base (a wineglass)

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 (5.1)
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 (5.2)
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 (5.3)
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 (5.4)
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 (5.5)

6. Cone with base (see above) and cover (a cap)

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 (6.1)
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 (6.2)
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 (6.3)
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 (6.4)
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 (6.5)

7. Cone with semisphere - Can you get the solution? And for others bodies!

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 (7.1)
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 (7.2)
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 (7.3)
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 (7.4)
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 (7.5)
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 (7.6)
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