Answer
$h(r)=\frac{300}{\pi r^2}$
Work Step by Step
The volume of a cone is $V=\frac{1}{3}\cdot b\cdot h$. We want a function to find $h$, so we solve for $h$ and substitute $V$ for $100$:
$3\cdot 100=3\cdot \frac{1}{3}\cdot b\cdot h$
$300\cdot \frac{1}{b}=b\cdot h \cdot \frac{1}{b}$
$h=\frac{300}{b}$
Now, we want the function in terms of $r$. We know that the base $b$ is the one of a circle which is $\pi r^2$, so we'll substitute it and we get the height as a function of the radius.
$h(r)=\frac{300}{\pi r^2}$
