STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $V = 510\, \text{cm}$ and $h = 13\, \text{cm}$ we have:

$$ 510\, \text{cm} = \dfrac{ 13\, \text{cm} ^{ 2 } \cdot r \cdot \pi}{ 3 } $$$$ 510\, \text{cm} \cdot 3 = 13\, \text{cm} ^{ 2 } \cdot r \cdot \pi $$$$ 1530\, \text{cm} = 169\, \text{cm}^2 \cdot r \cdot \pi $$$$ r = \dfrac{ 1530\, \text{cm} }{ 169\, \text{cm}^2 \, \pi} $$$$ r = 2.8817\, \text{cm}^-1 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $r = 2.8817\, \text{cm}^-1$ we have:

$$ d = 2 \cdot 2.8817\, \text{cm}^-1 $$ $$ d \approx 5.7635\, \text{cm}^-1 $$

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