STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $d = 6\, \text{cm}$ we have:

$$ 6\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 6\, \text{cm} }{ 2 } $$ $$ r = 3\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $V = 113.097\, \text{cm}$ and $r = 3\, \text{cm}$ we have:

$$ 113.097\, \text{cm} = \dfrac{ h ^{ 2 } \cdot \left( 3\, \text{cm} \right)^{4} \cdot \pi}{ 3 } $$$$ 113.097\, \text{cm} \cdot 3 = h ^{ 2 } \cdot \left( 3\, \text{cm} \right)^{4} \cdot \pi $$$$ 339.291\, \text{cm} = 3\, \text{cm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 339.291\, \text{cm}}{ 3\, \text{cm} \, \pi } $$$$ h ^{ 2 } \approx 35.9998 $$$$ h \approx \sqrt{ 35.9998 } $$$$ h \approx 6 $$

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