Answer
$d=12.0~in$
Work Step by Step
To find the diameter of the metal duct, we use the formula for the area of a circle:
$A=\frac{\pi*d^{2}}{4}$
where we have the area:
$A=113~in^{2}$
Solving for the diameter, $d$, gives:
$A=\frac{\pi*d^{2}}{4}$
$d=\sqrt {\frac{4A}{\pi}}=\sqrt {\frac{4(113in^{2})}{\pi}}=11.99~in\approx12.0~in$
