Question 2

A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in. squares from each corner and folding up the sides. The box is to hold $5408 \mathrm{in}^{3}$. How big a piece of cardboard is needed?

Your answer is:
in. by in.

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Step 1 ：Given that the volume of the box is \(5408 \mathrm{in}^{3}\), we can set up the equation \(l^2*2 = 5408\) and solve for \(l\).

Step 2 ：Once we have the value of \(l\), we can determine the size of the original piece of cardboard. The length and width of the original piece of cardboard are each \(l + 2*2\) (the length of the base plus twice the size of the squares cut from each corner).

Step 3 ：By solving the equation, we find that \(l = 52.0\).

Step 4 ：Therefore, the size of the original piece of cardboard is \(52.0 + 2*2 = 56.0\) in. by \(56.0\) in.

Step 5 ：Final Answer: The size of the piece of cardboard needed is \(\boxed{56}\) in. by \(\boxed{56}\) in.