Imagine the center of the equilateral triangle base sitting on the origin in the xy-plane. The figure comes to a point somewhere along the z-axis at the point (0,0,h).
The general formula for finding volume of such a figure is , where is the cross-sectional area of the figure at a distance r from the origin. Here, your bounds of integration will be . since it comes to a point, and since this is the area of an equilateral triangle with side length .
Since the side-length of the equilateral cross-sectional triangle shrinks linearly from a to 0, it can be represented as , so the area
And therein lies your integral:
(You can of course check your work by using the simple geometric formula for figures that start at a base of area b and rise to a point at height h.)