To find the volume of a cone that shares the same radius and height as a cylinder, we can use the formulas for their volumes:
The volume \( V \) of a cylinder is given by:
\[ V_{\text{cylinder}} = \pi r^2 h \]
The volume \( V \) of a cone is given by:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
Given that the volume of the cylinder is \( V_{\text{cylinder}} = 60 , \text{cm}^3 \), we can substitute into the formula for the cone.
Since the cone's volume is one-third that of the cylinder, we can calculate:
\[ V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}} = \frac{1}{3} \times 60 , \text{cm}^3 = 20 , \text{cm}^3 \]
Thus, the volume of the cone is 20 cm³.
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