Find the diameter $ d $ of a sphere if volume $V = 320$.

$d = 17.4808$

STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $ V = 320 $ we have:

$$ 320 = \dfrac{ 4 \cdot r^2 \cdot \pi }{ 3 }$$ $$ 320 \cdot 3 = 4 \cdot r^2 \cdot \pi $$ $$ 960 = 4 \cdot r^2 \cdot \pi $$ $$ r^2 \cdot \pi = \dfrac{ 960 }{ 4 } $$ $$ r^2 \cdot \pi = 240 $$ $$ r = \sqrt{ \frac{ 240 }{\pi} } $$ $$ r \approx 8.7404 $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $ r = 8.7404 $ we have:

$$ d = 2 \cdot 8.7404 $$ $$ d \approx 17.4808 $$

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