STEP 1: find radius $ r $

To find radius $ r $ use formula:

$$ d = 2 \cdot r $$

After substituting $d = 1\, \text{cm}$ we have:

$$ 1\, \text{cm} = 2 \cdot r $$ $$ r = \dfrac{ 1\, \text{cm} }{ 2 } $$ $$ r = \frac{ 1 }{ 2 }\, \text{cm} $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $r = \dfrac{ 1 }{ 2 }\, \text{cm}$ we have:

$$ V = \dfrac{ 4 \cdot \left( \frac{ 1 }{ 2 }\, \text{cm} \right)^{3} \cdot \pi}{ 3 } $$ $$ V = \dfrac{ 4 \cdot \frac{ 1 }{ 8 }\, \text{cm}^3 \cdot \pi}{ 3 }$$ $$ V = \dfrac{ \frac{ 1 }{ 2 }\, \text{cm}^3 \cdot \pi}{ 3 }$$ $$ V = \frac{ 1 }{ 6 }\, \text{cm}^3 \cdot \pi $$

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