## Elementary Technical Mathematics

$d=12.0~in$
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: $A=\frac{\pi*d^{2}}{4}$ $d=\sqrt {\frac{4A}{\pi}}=\sqrt {\frac{4(113in^{2})}{\pi}}=11.99~in\approx12.0~in$