To find radius $ r $ use formula:

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

After substituting $V = 500\, \text{cm}^2$ we have:

$$ 500\, \text{cm}^2 = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$ $$ 500\, \text{cm}^2 \cdot 3 = 4 \cdot r^3 \cdot \pi $$ $$ 1500\, \text{cm}^2 = 4 \cdot r^3 \cdot \pi $$ $$ r^3 \cdot \pi = \dfrac{ 1500\, \text{cm}^2 }{ 4 } $$ $$ r^3 \cdot \pi = 375\, \text{cm}^2 $$ $$ r = \sqrt[3]{ \frac{ 375\, \text{cm}^2 }{\pi} } $$ $$ r \approx 4.9237\, \text{cm} $$

Sphere Calculator