To find the volume of the solid using the given information, we can follow these steps:

Step 1: Determine the equation of the base

The base of the solid is an equilateral triangle with an altitude of 9 units. Since the triangle is equilateral, the length of each side can be determined using the formula for the height (altitude) of an equilateral triangle:

$\text{Height} = \frac{\sqrt{3}}{2} \times \text{side length}$

Given that the height is 9, we can solve for the side length $s$:

$9 = \frac{\sqrt{3}}{2} s$

$s = \frac{18}{\sqrt{3}} = 6\sqrt{3}$

Since the altitude lies along the $x$-axis and the left vertex of the triangle is at the origin, the vertices of the triangle are located at $(0, 0)$, $(9, 0)$, and $\left(\frac{9}{2}, 6\sqrt{3}\right)$.

Step 2: Determine the function for the base width

The width of the triangle at any height $x$ from the base (at $x = 0$) can be determined by the line equation. The length of the side perpendicular to the altitude at a distance $x$ from the base is given by:

[ \text{Width}(x) = 2 \times \text{length of the segment from the center to the edge}