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Mindy is a sculptor. She has a cylinder of stone with a radius of $3\,\text{m}$ and a height of $2\,\text{m}$. She needs to carve out a sphere of radius $1\,\text{m}$ from the cylinder. Mindy must cut away $\frac{v}{3}\pi\,\text{m}^{3}$ of stone from the cylinder in order to be left with the sphere. What is the value of $v$?$\newline$◻