Question

Volumul unui tetraedru reguat cu muchia de 3 cm este de cati cm la a 3-a ?

Answer 1

V = ( Aria bazei x inaltimea ) : 3

Aria bazei = $\frac{l^{2} \sqrt{3} }{4} = \frac{9 \sqrt{3} }{4}$

Inaltimea = $\frac{l \sqrt{6} }{3} = \frac{3 \sqrt{6} }{3} = \sqrt{6}$

V = $\frac{\frac{9 \sqrt{3} }{4}* \sqrt{6}}{3} = \frac{9 \sqrt{18} }{12} = \frac{27 \sqrt{2} }{12} = \frac{9 \sqrt{2} }{4}$ $cm^{3}$