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D = 3√2
V = ?
V = a³
D² = a² + d²
d = a√2 - przekątna kwadratu (podstawy)
D² = a² + (a√2)²
D² = a² + 2a²
D² = 3a²/:3
a² = D²/3
a = d√3/3
a = 3√2*√3/3
a = √6
V = (√6)³
V = 6√6
Odp: Objętość sześcianu wynosi 6√6.