The side length of the original cube for the given measurements and condition is equal to 8.6ft.
As given in the question,
Let 'x' be the side of the original cube.
Volume of original cube = x³
As given 8ft thick slice is cut from the top of the cube.
Volume of the thick slice = 8x²
Volume of the resulting rectangular box = 44
⇒ x³ - 8x² = 44
⇒ x³ - 8x² -44 =0
Plot the graph of the function.
Graph is attached.
From the graph approximate value of side length 'x' = 8.6 ft.
Therefore, the side length of the original cube is equal to 8.6ft.
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