To find radius $ r $ use formula:

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

After substituting $V = 4\, \text{cm}$ we have:

$$ 4\, \text{cm} = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$ $$ 4\, \text{cm} \cdot 3 = 4 \cdot r^3 \cdot \pi $$ $$ 12\, \text{cm} = 4 \cdot r^3 \cdot \pi $$ $$ r^3 \cdot \pi = \dfrac{ 12\, \text{cm} }{ 4 } $$ $$ r^3 \cdot \pi = 3\, \text{cm} $$ $$ r = \sqrt[3]{ \frac{ 3\, \text{cm} }{\pi} } $$ $$ r \approx 0.9847 $$

Sphere Calculator