#### Answer

$\approx$ 280.6 $cm^{3}$

#### Work Step by Step

Find the area of the base of the prism.
Each base of the triangular prism is an equilateral triangle. An altitude of the triangle divides it into two 30-60-90 triangles. The height of the triangle is $\sqrt 3$ x the shorter leg, which is 3$\sqrt 3$.
B=$\frac{1}{2}$bh
B=$\frac{1}{2}$(6)(3$\sqrt 3$)
B=9$\sqrt 3$
V=Bh
V=9$\sqrt 3$(18)
V=162$\sqrt 3$
V=280.5922308