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:
\[ V = \frac{1}{3} \pi r^2 h \]
Since the cone and the cylinder share the same radius \( r \) and height \( h \), we can relate their volumes. Given that the volume of the cylinder is 60 cm³, we can find the volume of the cone using the relationship:
\[ V_{\text{cone}} = \frac{1}{3} V_{\text{cylinder}} \]
Substituting the given volume of the cylinder:
\[ V_{\text{cone}} = \frac{1}{3} \times 60 \text{ cm}^3 = 20 \text{ cm}^3 \]
Therefore, the volume of the cone is 20 cm³.
1 answer