Question

a rectangular sheet of metal has identical squares cut from each corner. the sheet is then bent along the dotted lines to form an open box. the volume of the box is 420 \text{ in.}^3.

the equation 4x^3 - 72x^2 + 320x = 420 can be used to find x, the side length of the square cut from each corner.

what is the side length of the square that is cut from each corner, to the nearest inch?

in.

Explanation:

Set up the polynomial equation

$$ 4x^3 - 72x^2 + 320x - 420 = 0 $$

$$ x^3 - 18x^2 + 80x - 105 = 0 $$

Test integer values for x within physical constraints

$$
LATEXBLOCK0
$$

Verify the physical solution

$$
LATEXBLOCK1
$$

Answer:

What is the side length of the square that is cut from each corner, to the nearest inch?
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