To find the volume of a cylinder that has the same radius and height as a cone with a given volume, we first need to understand the formula for the volume of a cone and a cylinder.
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The volume \( V \) of a cone is given by the formula: \[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
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The volume \( V \) of a cylinder is given by the formula: \[ V_{\text{cylinder}} = \pi r^2 h \]
From the problem, we know the volume of the cone is 27 cm³. Therefore, we can represent it as: \[ \frac{1}{3} \pi r^2 h = 27 \]
To find the volume of the cylinder that shares the same radius and height, we can multiply both sides of the cone's volume equation by 3: \[ \pi r^2 h = 3 \times 27 = 81 \]
Thus, the volume of the cylinder is: \[ V_{\text{cylinder}} = \pi r^2 h = 81 \text{ cm}^3 \]
Therefore, the volume of the cylinder is 81 cm³.