To find height $ h $ use formula:

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

After substituting $V = 301.44\, \text{cm}$ and $r = 6\, \text{cm}$ we have:

$$ 301.44\, \text{cm} = \dfrac{ h ^{ 2 } \cdot \left( 6\, \text{cm} \right)^{4} \cdot \pi}{ 3 } $$$$ 301.44\, \text{cm} \cdot 3 = h ^{ 2 } \cdot \left( 6\, \text{cm} \right)^{4} \cdot \pi $$$$ 904.32\, \text{cm} = 6\, \text{cm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 904.32\, \text{cm}}{ 6\, \text{cm} \, \pi } $$$$ h ^{ 2 } \approx 47.9756 $$$$ h \approx \sqrt{ 47.9756 } $$$$ h \approx 6.9264 $$

Cone Calculator