To find radius $ r $ use formula:

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

After substituting $V = 678.24\, \text{cm}$ and $h = 6\, \text{cm}$ we have:

$$ 678.24\, \text{cm} = \dfrac{ 6\, \text{cm} ^{ 2 } \cdot r \cdot \pi}{ 3 } $$$$ 678.24\, \text{cm} \cdot 3 = 6\, \text{cm} ^{ 2 } \cdot r \cdot \pi $$$$ 2034.72\, \text{cm} = 36\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 2034.72\, \text{cm} }{ 36\, \text{cm}^2 \, \pi} $$$$ r = 17.9909\, \text{cm}^-1 $$

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