#### Answer

Domain: $[0, \sqrt[3] \frac{3}{4\pi}]$
Independent Variable: $r$ (the radius of the balloon)
Dependent Variable: $V$ (the volume of the balloon)

#### Work Step by Step

The volume of a balloon is given by $f(r) = \frac{4}{3}\pi r^3$.
The maximum volume is $1$ $m^3$. The value of $r$ that yields us $1$ $m^3$ is $\sqrt[3] \frac{3}{4\pi}$, meaning that the radius can range from $0$ through $\sqrt[3] \frac{3}{4\pi}$.
An independent variable is a variable we can change. Thus $r$, the radius of the balloon, is the independent variable.
A dependent variable is a variable that changes when the independent variable variable changes. Thus, $V$, the volume of the balloon, is the dependent variable.