Question

O piramida triunghiulara regulata are aria laterala de 195√3 cm² si aria totala de 270√3 cm². Calculati volumul piramidei.

Answer 1

At=Al+Ab
270$\sqrt{3}$=195$\sqrt{3}$+Ab
Ab=270$\sqrt{3}$-195$\sqrt{3}$
Ab=75[tex] \sqrt{3 } [/tex]
Ab=$\frac{ l^{2} \sqrt{3} }{4}=75 \sqrt{3}$
In final$l^{2} =10 \sqrt{3}$
OM=$\frac{1}{3}* \frac{10 \sqrt{3}* \sqrt{3} }{2} =5$
$Al=\frac{Pb*ap }{2} Pb=195 \sqrt{3} ; VO=13$[tex]VO^{2}= 13^{2} - 5^{2} ;VO=12[/tex]$V= \frac{Ab*h}{3}= \frac{75 \sqrt{3}*12 }{3} .Se simplifica iar in final V=300 \sqrt{3} cm^{3}$