The volume of a cylinder is given by:
[tex]V=h\pi r^2[/tex]
In this case the volume is 100 cubic inches and the height is 12 inches; plugging this values in the equation above and solving for r we have:
[tex]\begin{gathered} 100=12\pi r^2 \\ r^2=\frac{100}{12\pi} \\ r=\sqrt[]{\frac{100}{12\pi}} \\ r=1.6 \end{gathered}[/tex]
Therefore the radius is 1.6 inches.
