The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
In this case, we know that:
\[ V = 100\pi \quad \text{and} \quad h = 12 \]
Substituting these values into the volume formula:
\[ 100\pi = \frac{1}{3} \pi r^2 (12) \]
We can simplify this equation. First, cancel \( \pi \) from both sides:
\[ 100 = \frac{1}{3} r^2 (12) \]
Next, simplify \( \frac{1}{3} (12) \):
\[ 100 = 4r^2 \]
Now, solve for \( r^2 \):
\[ r^2 = \frac{100}{4} = 25 \]
Taking the square root of both sides gives:
\[ r = \sqrt{25} = 5 \]
Thus, the radius of the cone is
\[ \boxed{5} \text{ inches.} \]