To find height $ h $ use formula:

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

After substituting $V = 6782.4\, \text{cm}$ and $r = 18\, \text{cm}$ we have:

$$ 6782.4\, \text{cm} = \dfrac{ h ^{ 2 } \cdot \left( 18\, \text{cm} \right)^{4} \cdot \pi}{ 3 } $$$$ 6782.4\, \text{cm} \cdot 3 = h ^{ 2 } \cdot \left( 18\, \text{cm} \right)^{4} \cdot \pi $$$$ 20347.2\, \text{cm} = 18\, \text{cm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 20347.2\, \text{cm}}{ 18\, \text{cm} \, \pi } $$$$ h ^{ 2 } \approx 359.8167 $$$$ h \approx \sqrt{ 359.8167 } $$$$ h \approx 18.9688 $$

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