Answer
$\color{blue}{V=\dfrac{4\pi}{3}r^3}$
Work Step by Step
RECALL:
(1) If $y$ varies directly as $x$, then $y=kx$ where $k$ is the constant of proportionality.
(2) If $y$ varies inversely as $x$, then $y=\dfrac{k}{x}$ where $k$ is the constant of proportionality.
Notice that when the variation is direct, the variable is on the numerator while if the variation is inverse, the variable is in the denominator.
The volume $V$ varies directly with the cube of the radius $r$ with a constant of proportionality $k$ of $\frac{4\pi}{3}$.
Thus, the equation of the variation is:
$\color{blue}{V=\dfrac{4\pi}{3}r^3}$
