To find volume $ V $ use formula:
$$ V = \dfrac{ 4 \cdot r^3 \cdot \pi}{ 3 } $$After substituting $r = 1\, \text{mm}$ we have:
$$ V = \dfrac{ 4 \cdot \left( 1\, \text{mm} \right)^{3} \cdot \pi}{ 3 } $$ $$ V = \dfrac{ 4 \cdot 1\, \text{mm}^3 \cdot \pi}{ 3 }$$ $$ V = \dfrac{ 4\, \text{mm}^3 \cdot \pi}{ 3 }$$ $$ V = \frac{ 4 }{ 3 }\, \text{mm}^3 \cdot \pi $$