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:
\[ V = \pi r^2 h \]
Since the cone and the cylinder have the same base radius ( \( r \) ) and height ( \( h \) ), we can express the volume of the cylinder in relation to the volume of the cone.
From the volume of the cone, we know:
\[ 10 = \frac{1}{3} \pi r^2 h \]
To find the volume of the cylinder, we use the volume formula for the cylinder:
\[ V_{cylinder} = \pi r^2 h \]
We can see that the volume of the cylinder is three times that of the cone:
\[ V_{cylinder} = 3 \times \text{Volume of cone} = 3 \times 10 = 30 \text{ cubic units} \]
Thus, the volume of the cylinder is:
\[ \boxed{30 \text{ cubic units}} \]