The volume of a cylinder is given by the formula:
\[ V_{\text{cylinder}} = \pi r^2 h \]
The volume of a cone, which shares the same radius \( r \) and height \( h \) as the cylinder, is given by the formula:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Since the volume of the cylinder is 60 cm³, we can express the volume of the cone in relation to the cylinder's volume:
\[ V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}} = \frac{1}{3} \times 60 \text{ cm}^3 = 20 \text{ cm}^3 \]
Therefore, the volume of the cone that shares the same radius and height as the cylinder is:
\[ \text{20 cm}^3 \]
Answer: 20 cm³