To solve this problem, we need to use the formulas for the volume of a cylinder and a cone.
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Volume of a Cylinder (\( V_c \)): \[ V_c = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.
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Volume of a Cone (\( V_{cone} \)): \[ V_{cone} = \frac{1}{3} \pi r^2 h \]
Given that the cone is carved out of the cylinder and they share the same radius \( r \) and height \( h \), we can express the remaining volume after carving the cone out of the cylinder as follows:
\[ \text{Volume remaining} = V_c - V_{cone} \]
Substituting in the formulas for the volumes:
\[ \text{Volume remaining} = \pi r^2 h - \frac{1}{3} \pi r^2 h \]
Factoring out \( \pi r^2 h \):
\[ \text{Volume remaining} = \pi r^2 h \left(1 - \frac{1}{3}\right) = \pi r^2 h \left(\frac{2}{3}\right) \]
Given that the volume remaining is \( 144 , \text{in}^3 \):
\[ \frac{2}{3} \pi r^2 h = 144 \]
To find the original volume of the cylinder:
\[ V_c = \pi r^2 h = \frac{3}{2} \times 144 = 216 , \text{in}^3 \]
Thus, the volume of the original cylinder is:
\[ \boxed{216 , \text{in}^3} \]