Question

Calcule o volume de uma pirâmide regular hexagonal de altura 5m e aresta da base 4 raiz de 3m

Answer 1

$\textbf{Dados:}\\\\ \mathrm{\Rightarrow Altura\ \to\ h=5\ m}\\ \mathrm{\Rightarrow Aresta\ da\ base\ \to\ a=4\sqrt{3}\ m}\\\\ \textbf{Resolu\c{c}\~ao:}\\\\ \mathrm{\Rightarrow Calculando\ a\ \acute{a}rea\ da\ base\ (hex\acute{a}gono\ regular)\ \to}\\\\ \mathrm{\to\ A_b=\dfrac{3a^2\sqrt{3}}{2}=\dfrac{3(4\sqrt{3})^2\sqrt{3}}{2}=\dfrac{3.16.3.\sqrt{3}}{2}=\boxed{\mathrm{72\sqrt{3}\ m^2}}}\\\\ \mathrm{\Rightarrow Calculando\ o\ volume\ da\ pir\hat{a}mide\ \to\ V=\dfrac{A_b.h}{3}=}\\\\ \mathrm{=\dfrac{72\sqrt{3}.5}{3}=24\sqrt{3}.5\ \to\ \boxed{\mathbf{V=120\sqrt{3}\ m^3}}}$