Find the volume $ V $ of a sphere if area $A = 615.44$.

$V = 65.3001\pi$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $ A = 615.44 $ we have:

$$ 615.44 = 4 \cdot r^2 \cdot \pi $$ $$ r^2 \cdot \pi = \dfrac{ 615.44 }{ 4 } $$ $$ r^2 \cdot \pi = 153.86 $$ $$ r = \sqrt{ \frac{ 153.86 }{\pi} } $$ $$ r \approx 6.9982 $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

$$ V = \dfrac{ 4 \cdot r^2 \cdot \pi}{ 3 } $$

After substituting $ r = 6.9982 $ we have:

$$ V = \dfrac{ 4 \cdot 6.9982^2 \cdot \pi}{ 3 } $$ $$ V = \dfrac{ 4 \cdot 48.975 \cdot \pi}{ 3 }$$ $$ V = \dfrac{ 195.9002 \cdot \pi}{ 3 }$$ $$ V = 65.3001 \cdot \pi $$

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