To find height $ h $ use formula:

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

After substituting $V = 180\pi\, \text{cm}$ and $r = 6\, \text{cm}$ we have:

$$ 180\pi\, \text{cm} = \dfrac{ h ^{ 2 } \cdot \left( 6\, \text{cm} \right)^{4} \cdot \pi}{ 3 } $$$$ 180\pi\, \text{cm} \cdot 3 = h ^{ 2 } \cdot \left( 6\, \text{cm} \right)^{4} \cdot \pi $$$$ 540\pi\, \text{cm} = 6\, \text{cm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 540\pi\, \text{cm}}{ 6\, \text{cm} \, \pi } $$$$ h ^{ 2 } = 90 $$$$ h = \sqrt{ 90 } $$$$ h = 3 \sqrt{ 10 } $$

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