Question

v = l·w·h = 4x²
4x² = 8464
\frac{4x²}{4}=\frac{8464}{4}
sqrt{x²}=sqrt{2116}
x = 46in
46in by 46in

Explanation:

Step1: Write volume formula

The volume formula for a rectangular - box is $V = l\times w\times h$. Here, assuming the base of the box has side - length $x$ (after cutting 4 - inch squares from the corners of a square sheet) and height $h = 4$ inches, and $V=8464$ cubic inches. So $V = 4x^{2}=8464$.

Step2: Solve for $x^{2}$

Divide both sides of the equation $4x^{2}=8464$ by 4. We get $x^{2}=\frac{8464}{4}=2116$.

Step3: Solve for $x$

Take the square root of both sides. $\sqrt{x^{2}}=\sqrt{2116}$, so $x = 46$ inches.

Answer:

The original square sheet has dimensions 46 inches by 46 inches.