要用圆形铁片截出边长为 $4 \mathrm{~cm}$ 的正方形铁片, 则选用的圆形铁片的直径最小是 ( )
如图所示,

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$\because$ 四边形 $A B C D$ 是正四边形,

$\therefore \angle B O C=\left(\frac{360}{4}\right)^{\circ}=90^{\circ} ;$

$\because O B=O C, O E \perp B C$

$\therefore \angle B O E=\frac{1}{2} \angle B O C=45^{\circ}, B E=C E=O E=\frac{1}{2} A B=2 \mathrm{~cm}$,

$\therefore 2 O B=2 \sqrt{O E^{2}+B E^{2}}=2 \sqrt{2^{2}+2^{2}}=4 \sqrt{2} \mathrm{~cm}$,

$\therefore$ 选用的圆形铁片的直径最小要 $4 \sqrt{2} \mathrm{~cm}$.

故选 $D$.