To find radius $ r $ use formula:

$$ V = \dfrac{ h ^{ 2 } \cdot r \cdot \pi}{ 3 } $$

After substituting $V = 192\pi\, \text{cm}$ and $h = 20\, \text{cm}$ we have:

$$ 192\pi\, \text{cm} = \dfrac{ 20\, \text{cm} ^{ 2 } \cdot r \cdot \pi}{ 3 } $$$$ 192\pi\, \text{cm} \cdot 3 = 20\, \text{cm} ^{ 2 } \cdot r \cdot \pi $$$$ 576\pi\, \text{cm} = 400\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 576\pi\, \text{cm} }{ 400\, \text{cm}^2 \, \pi} $$$$ r = \frac{ 36 }{ 25 }\, \text{cm}^-1 $$

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