To find the volume of the cylinder when we know the volume of the cone, we can use the formulas for the volumes of both shapes.
The formula for the volume \( V \) of a cone is given by:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
The formula for the volume of a cylinder is:
\[ V_{\text{cylinder}} = \pi r^2 h \]
Given that the volume of the cone is \( 10\pi \) cubic units, we can set up the equation:
\[ \frac{1}{3} \pi r^2 h = 10\pi \]
To eliminate \( \pi \), we divide both sides by \( \pi \):
\[ \frac{1}{3} r^2 h = 10 \]
Multiplying both sides by 3 gives:
\[ r^2 h = 30 \]
Now, substituting \( r^2 h \) into the cylinder's volume formula:
\[ V_{\text{cylinder}} = \pi r^2 h = \pi(30) = 30\pi \]
Thus, the volume of the cylinder is:
\[ \boxed{30\pi} \text{ cubic units} \]