STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $V = 320\, \text{cm}$ we have:

$$ 320\, \text{cm} = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$ $$ 320\, \text{cm} \cdot 3 = 4 \cdot r^3 \cdot \pi $$ $$ 960\, \text{cm} = 4 \cdot r^3 \cdot \pi $$ $$ r^3 \cdot \pi = \dfrac{ 960\, \text{cm} }{ 4 } $$ $$ r^3 \cdot \pi = 240\, \text{cm} $$ $$ r = \sqrt[3]{ \frac{ 240\, \text{cm} }{\pi} } $$ $$ r \approx 4.2431 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $r = 4.2431\, \text{cm}^0$ we have:

$$ d = 2 \cdot 4.2431 $$ $$ d \approx 8.4863 $$

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