Finding the constant that results in the volume of the solid

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Good afternoon, I came across the following problem and I couldn't find a way to solve it

"Given the following pieces of information:

$a>0$

$R=${$(x,y) \in \mathbb{R}^2|x \geq 0,a \leq y\leq −ln(ax)$}, where $S$ is a solid obtained by the revolution of the area $R$ around the $x$ axis

find the value of $a$, knowing that the volume of $S$ is equal to $4$"

I tried to integrate and apply the method to find the volume of the solids of revolution but I can never get rid of this constant a Does anyone know how I can solve this problem?