I think CPhill has assumed that the base is an equilateral triangle of side length 18 units.
This is not actually stated in the question but i guess it is a reasonable assumption.
All the angels are 60 degrees
----------------------
in triangle ABC
$${\mathtt{Area}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{a}}{\mathtt{\,\times\,}}{\mathtt{b}}{\mathtt{\,\times\,}}{\mathtt{sinC}}$$
$${\mathtt{Area}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\times\,}}{\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{sin60}}$$
$${\mathtt{Area}} = {\frac{{\mathtt{162}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}$$
$${\mathtt{Area}} = {\mathtt{81}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}$$
---------------------------------------
$${\mathtt{Volume}} = {\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{Area}}{\mathtt{\,\times\,}}{\mathtt{height}}$$
$${\mathtt{Volume}} = {\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{81}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{4}}$$
$${\mathtt{Volume}} = {\mathtt{108}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}$$ units cubed. 
$$Volume \approx 187unit^3$$
.