To find radius $ r $ use formula:

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

After substituting $V = 6000\, \text{cm}^2$ we have:

$$ 6000\, \text{cm}^2 = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$ $$ 6000\, \text{cm}^2 \cdot 3 = 4 \cdot r^3 \cdot \pi $$ $$ 18000\, \text{cm}^2 = 4 \cdot r^3 \cdot \pi $$ $$ r^3 \cdot \pi = \dfrac{ 18000\, \text{cm}^2 }{ 4 } $$ $$ r^3 \cdot \pi = 4500\, \text{cm}^2 $$ $$ r = \sqrt[3]{ \frac{ 4500\, \text{cm}^2 }{\pi} } $$ $$ r \approx 11.2725\, \text{cm} $$

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