Question

calcule o volume do prisma abaixo sabendo que suas bases são regulares. Consideres /3 = 1,7 A)510000 cm3 B)480000 cm3 C)17430 cm3 D)12760 M3
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Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm C\acute alculo\,da\,\acute area\,da\,base\, B:}\\\sf B=\dfrac{3\cdot \ell^2\sqrt{3}}{2},onde\,\ell~\acute e\,o\,lado\,do\,hex\acute agono.\\\\\sf B=\dfrac{3\cdot 20^2\sqrt{3}}{2}\\\\\sf B=\dfrac{3\cdot\diagdown\!\!\!\!\!\!\!40\!\diagdown\!\!\!0\sqrt{3}}{\diagdown\!\!\!2}\\\\\sf B=3\cdot200\sqrt{3}\\\sf B=600\sqrt{3}\,cm^2.\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm C\acute alculo\,do\,volume:}\\\sf V=B\cdot H,onde\,B~\acute e~a~\acute area\,da\,base\\\sf e\,H\,a\,altura\,do\,prisma.\\\sf V=600\sqrt{3}\cdot 50\\\sf V=30~000\sqrt{3}\\\sf V=30~000\cdot1,7\\\sf V=51000\,cm^3\end{array}}$