Intermediate Algebra (12th Edition)

$\text{The volume of a sphere varies directly as the cube of its radius.}$
Recall: (1) When $y$ varies directly as $x$, the direct variation's equation is $y=kx$ where $k$ is the constant of variation. (2) When $y$ varies inversely as $x$, the inverse variation's equation is $y=\frac{k}{x}$ or $xy=k$ where $k$ is the constant of variation. In the equation $V=\frac{4}{3}\pi{r^3}$, $V$ varies directly as $r^3$ with a constant of variation of $\frac{4}{3}\pi$. Thus: $\text{The volume of a sphere varies directly as the cube of its radius.}$