Question

5. No prisma hexagonal regular, cuja aresta da base mede 2 cm e altura medindo 5 cm.
Seu volume é:
H
a) 6√3 cm²
b) 30 cm²
c) 6(2√3+5) cm²
d) 30√3 cm³

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm \acute Area\,da\,base\,do\,pol\acute igono\,hexagonal}\\\rm B=\dfrac{3l^2\sqrt{3}}{2}\\\underline{\rm Volume\,do\,prisma}\\\sf V=B\cdot h\\\tt dados\begin{cases}\sf l=2\,cm\\\sf h=5\,cm\\\sf V=?\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm C\acute alculo\,da\,\acute area\,da\,base:}\\\sf B=\dfrac{3l^2\sqrt{3}}{2}\\\\\sf B=\dfrac{3\cdot2^2\sqrt{3}}{2}\\\\\sf B=\dfrac{3\cdot\backslash\!\!\!4\sqrt{3}}{\backslash\!\!\!2}\\\\\sf B=3\cdot2\sqrt{3}\\\sf B=6\sqrt{3}\,cm^2\\\underline{\rm C\acute alculo\,do\,volume:}\\\sf V=B\cdot h\\\sf V=6\sqrt{3}\cdot 5\\\sf V=30\sqrt{3}\,cm^3\\\Huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$