To find height $ h $ use formula:

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

After substituting $V = 100\, \text{cm}$ and $r = 5\, \text{cm}$ we have:

$$ 100\, \text{cm} = \dfrac{ h ^{ 2 } \cdot \left( 5\, \text{cm} \right)^{4} \cdot \pi}{ 3 } $$$$ 100\, \text{cm} \cdot 3 = h ^{ 2 } \cdot \left( 5\, \text{cm} \right)^{4} \cdot \pi $$$$ 300\, \text{cm} = 5\, \text{cm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 300\, \text{cm}}{ 5\, \text{cm} \, \pi } $$$$ h ^{ 2 } \approx 19.0985 $$$$ h \approx \sqrt{ 19.0985 } $$$$ h \approx 4.3702 $$

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