Answer
$\color{blue}{V=\dfrac{4}{3}{\pi}{x^3}}$
Work Step by Step
$V$ varies directly with $x^3$, so the equation that represents the variation is:
$V=kx^3$
Since $V=36\pi$ when $x=3$ , substituting these into the tentative equation above gives:
$V=kx^3
\\36\pi=k(3^3)
\\36\pi=k(27)
\\\frac{36\pi}{27} = k
\\\frac{4\pi}{3}=k$
Thus, the equation of the direct variation is:
$\color{blue}{V=\dfrac{4}{3}{\pi}{x^3}}$
