To find the radius of the cone, we can use the formula for the volume of a cone, which is given by:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given that the volume \( V = 100\pi \) cubic inches and the height \( h = 12 \) inches, we can substitute these values into the formula:
\[ 100\pi = \frac{1}{3} \pi r^2 (12) \]
We can simplify this equation by first canceling out \( \pi \) from both sides:
\[ 100 = \frac{1}{3} r^2 (12) \]
Now simplify the right side:
\[ 100 = 4r^2 \]
Next, solve for \( r^2 \):
\[ r^2 = \frac{100}{4} = 25 \]
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{25} = 5 \]
Therefore, the radius of the cone is
\[ \boxed{5} \text{ inches.} \]