STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $d = 15\, \text{cm}$ we have:

$$ 15\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 15\, \text{cm} }{ 2 } $$ $$ r = \frac{ 15 }{ 2 }\, \text{cm} $$

STEP 2: find height $ h $

To find height $ h $ use formula:

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

After substituting $V = 5298.75\, \text{cm}$ and $r = \dfrac{ 15 }{ 2 }\, \text{cm}$ we have:

$$ 5298.75\, \text{cm} = \frac{ 15 }{ 2 }\, \text{cm} \cdot h ^{ 2 } \cdot \pi $$$$ h ^{ 2 } = \dfrac{ 5298.75\, \text{cm}}{ \frac{ 15 }{ 2 }\, \text{cm} \, \pi } $$$$ h ^{ 2 } \approx 224.8854 $$$$ h \approx \sqrt{ 224.8854 } $$$$ h \approx 14.9962 $$

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