STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ V = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$

After substituting $V = 616\, \text{ft}^2$ we have:

$$ 616\, \text{ft}^2 = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$ $$ 616\, \text{ft}^2 \cdot 3 = 4 \cdot r^3 \cdot \pi $$ $$ 1848\, \text{ft}^2 = 4 \cdot r^3 \cdot \pi $$ $$ r^3 \cdot \pi = \dfrac{ 1848\, \text{ft}^2 }{ 4 } $$ $$ r^3 \cdot \pi = 462\, \text{ft}^2 $$ $$ r = \sqrt[3]{ \frac{ 462\, \text{ft}^2 }{\pi} } $$ $$ r \approx 5.2783\, \text{ft} $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $r = 5.2783\, \text{ft}$ we have:

$$ d = 2 \cdot 5.2783\, \text{ft} $$ $$ d \approx 10.5567\, \text{ft} $$

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