STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $A = 144\pi\, \text{cm}$ we have:

$$ 144\pi\, \text{cm} = 4 \cdot r^2 \cdot \pi $$ $$ r^2 \cdot \pi = \dfrac{ 144\pi\, \text{cm} }{ 4 } $$ $$ r^2 \cdot \pi = 36\pi\, \text{cm} $$ $$ r^2 = 36 $$ $$ r = \sqrt{ 36 } $$ $$ r = 6 $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $r = 6\, \text{cm}^0$ we have:

$$ V = \dfrac{ 4 \cdot 6 \cdot \pi}{ 3 } $$ $$ V = \dfrac{ 4 \cdot 216 \cdot \pi}{ 3 }$$ $$ V = \dfrac{ 864 \cdot \pi}{ 3 }$$ $$ V = 288 \cdot \pi $$

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