SOLUTION: Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square

Question 1114845: Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm^3.
Please help.
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52796) (Show Source): You can put this solution on YOUR website!
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After folding, you get an open box. Its base is the square with the side length of (x-2*4) = x-8 cm, where x is the side of the original cardboard. The height of the box is 4 cm. Hence, 4*(x-8)^2 = 144 is the volume equation. It gives (x-8)^2 = = 36. Hence, x-8 = = 6. Then x = 6+8 = 14. Answer. The side length of the original square piece of cardboard is 14 cm.

Solved.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. Then it was folded into an open-top box. Find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm^3.
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Area of original square:: x^2
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Area of base of box:: (x-8)^2
height of box:: 4 cm
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Equation:
4(x-8)^2 = 144 cm^3
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(x-8)^2 = 26
x-8 = sqrt(26)
x = 8+sqrt(26)
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Answer:: original dimensions are 8+sqrt(26) squared
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Cheers,
Stan H.
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