The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
If the cylinder has a volume of 60 cm³, that means:
\[ \pi r^2 h = 60 \text{ cm}^3 \]
To find the volume of the cone with the same radius and height, we use the cone's volume formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Substituting the expression for the cylinder's volume:
\[ V = \frac{1}{3} \times 60 \text{ cm}^3 \]
Calculating this gives:
\[ V = 20 \text{ cm}^3 \]
Thus, the volume of the cone that shares the same radius and height as the cylinder is \( \boxed{20 \text{ cm}^3} \).
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