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