Răspuns:
Explicație pas cu pas:
[tex]V=\frac{A_{b}\cdot h}{3}[/tex]
[tex]A_{b}=\frac{a^{2}\sqrt{3} }{4}[/tex]
[tex]a_{b}=\frac{a\sqrt{3} }{2}[/tex]
AO inaltime
OB=[tex]\frac{2}{3} \cdot a_{b}=\frac{2}{3} \cdot \frac{a\sqrt{3} }{2}=\frac{a\sqrt{3} }{3}[/tex]
Aplicam Pitagora in ΔAOB
[tex]a^{2} =\frac{3a^{2} }{9} +h^{2}[/tex]
[tex]h^{2}=a^{2} -\frac{3a^{2} }{9} =\frac{6a^{2} }{9} \\h=\frac{a\sqrt{6} }{3}[/tex]
[tex]V=\frac{A_{b}\cdot h}{3}=\frac{\frac{a^{2}\sqrt{3} }{4}\cdot\frac{a\sqrt{6} }{3} }{3} =\frac{3a^{3}\sqrt{2} }{36} =\frac{a^{3}\sqrt{2} }{12}[/tex]
