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Victoria C.
matematika

Matematická otázka

tři kovové koule s objemy v1=35 cm3, v2=55cm3 a v3=65cm3 se ulila jedna koule. Určete její povrch. Mám výpočet a výsledek, ale stále to proste nechapu a potřebovala bych přesný postup jak na to.

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MILAN K.
MILAN K. Contact
Snadno : odmocnina je tam na toto: ve třírozměrném prostoru je objem koule 4/3 pi * R^3, ale povrch je dV/dR = 3 * (4/3) * pi * R^ (3-1) = 4 * pi * R^ 2 Kdyby to bylo ve čtyřrozměrném prostoru, pak V (koule E4) = (1/2) * pi ^2 * R ^ 4 , pak S = dV/dR = 4 * (1/2) * pi^ 2 * R^ (4-1) = 2 * pi ^ 2 * R ^ 3 . Takže chceme vlastně v našem třírozměrném prostoru vyjádřit povrch nové koule pomocí jejího nového objemu a ten nový (větší) objem je funkcí nového (většího) poloměru . Nihil aliud. Prostě odtrojmocníme ten nový objem (spolu s konstantami) a máme nový poloměr a ten nový poloměr (spolu s konstantami) pak povýšíme na druhou :
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Michaela P.
Michaela P. Contact
Dobrý den, zkusila jsem Vám výpočet více rozepsat.
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