To find the volume of the cylinder, we start with the formula for the volume of a cone and a cylinder.
The volume \( V \) of a cone is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
The volume \( V \) of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
Since the cone and the cylinder have the same base radius \( r \) and the same height \( h \), we can see that the volume of the cylinder is three times the volume of the cone:
\[ V_{\text{cylinder}} = 3 \times V_{\text{cone}} \]
Given that the volume of the cone is \( 10\pi \) cubic units:
\[ V_{\text{cylinder}} = 3 \times 10\pi = 30\pi \text{ cubic units} \]
Therefore, the volume of the cylinder is:
\[ \boxed{30\pi} \text{ cubic units} \]