Find the volume $ V $ of a sphere if area $A = 200.96$.

$V = 21.3225\pi$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $ A = 200.96 $ we have:

$$ 200.96 = 4 \cdot r^2 \cdot \pi $$ $$ r^2 \cdot \pi = \dfrac{ 200.96 }{ 4 } $$ $$ r^2 \cdot \pi = 50.24 $$ $$ r = \sqrt{ \frac{ 50.24 }{\pi} } $$ $$ r \approx 3.999 $$

STEP 2: find volume $ V $

To find volume $ V $ use formula:

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

After substituting $ r = 3.999 $ we have:

$$ V = \dfrac{ 4 \cdot 3.999^2 \cdot \pi}{ 3 } $$ $$ V = \dfrac{ 4 \cdot 15.9919 \cdot \pi}{ 3 }$$ $$ V = \dfrac{ 63.9674 \cdot \pi}{ 3 }$$ $$ V = 21.3225 \cdot \pi $$

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