The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.
Given that the volume of the cone is \( 100\pi \) cubic inches and the height \( h \) is 12 inches, we can set up the equation:
\[ 100\pi = \frac{1}{3} \pi r^2 (12) \]
Now, simplify the equation:
\[ 100\pi = 4\pi r^2 \]
Next, divide both sides by \( \pi \):
\[ 100 = 4r^2 \]
Now, divide both sides by 4:
\[ 25 = r^2 \]
Finally, take the square root of both sides to find \( r \):
\[ r = 5 \]
Thus, the radius of the cone is \( \boxed{5} \) inches.