## College Algebra (10th Edition)

$\color{blue}{V=\dfrac{4}{3}{\pi}{x^3}}$
$V$ 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: $\color{blue}{V=\dfrac{4}{3}{\pi}{x^3}}$