STEP 1: find radius $ r $

To find radius $ r $ use formula:

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

After substituting $A = 400\, \text{in}^3$ we have:

$$ 400\, \text{in}^3 = 4 \cdot r^2 \cdot \pi $$ $$ r^2 \cdot \pi = \dfrac{ 400\, \text{in}^3 }{ 4 } $$ $$ r^2 \cdot \pi = 100\, \text{in}^3 $$ $$ r = \sqrt{ \frac{ 100\, \text{in}^3 }{\pi} } $$ $$ r \approx 5.6419\, \text{in} $$

STEP 2: find diameter $ d $

To find diameter $ d $ use formula:

$$ d = 2 \cdot r $$

After substituting $r = 5.6419\, \text{in}$ we have:

$$ d = 2 \cdot 5.6419\, \text{in} $$ $$ d \approx 11.2838\, \text{in} $$

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