STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $V = 36\pi\, \text{mm}^2$ we have:

$$ 36\pi\, \text{mm}^2 = \dfrac{ 4 \cdot r^3 \cdot \pi }{ 3 }$$ $$ 36\pi\, \text{mm}^2 \cdot 3 = 4 \cdot r^3 \cdot \pi $$ $$ 108\pi\, \text{mm}^2 = 4 \cdot r^3 \cdot \pi $$ $$ r^3 \cdot \pi = \dfrac{ 108\pi\, \text{mm}^2 }{ 4 } $$ $$ r^3 \cdot \pi = 27\pi\, \text{mm}^2 $$ $$ r^3 = 27 $$ $$ r = \sqrt[3]{ 27 } $$ $$ r = 3\, \text{mm} $$

STEP 2: find area $ A $

To find area $ A $ use formula:

$$ A = 4 \cdot r^2 \cdot \pi $$

After substituting $r = 3\, \text{mm}$ we have:

$$ A = 4 \cdot \left( 3\, \text{mm} \right)^{2} \cdot \pi $$ $$ A = 36\, \text{mm}^2 \cdot \pi $$ $$ A = 36\, \text{mm}^2 \cdot \pi $$

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