A square paper of side 10 cm is folded sequentially and a circular cut of radius 1 cm is made at the corners as shown below. After unfolding the sheet completely, what will be the total area of all the pieces which have been cut-out from the original square sheet? Assume the value of $\pi$ = 3.14.
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Unfolding can be modeled as geometric reflections. Reflections conserve area, so the total area of the cut-out shapes is simply the area cut out from a single layer multiplied by the total number of layers.
Step 1: Count the holes after unfolding. Each corner cut on the folded sheet reopens into 4 separate circular holes when the paper is fully unfolded. Step 2: Sum the areas. Area per circle $=\pi r^2=3.14\times1^2=3.14$ cm$^2$; with 4 holes the total $=4\times3.14$. \[ \boxed{12.56 \text{ cm}^2} \]
