Final answer:
The maximum volume created from the given piece of paper is 28 square inches.
Step-by-step explanation:
To find the maximum volume created from a piece of paper measuring 8.5 inches by 11 inches, we need to cut identical squares out of each corner. Let's assume the side length of the square we cut out is 'x' inches. The resulting dimensions of the paper will be (8.5 - 2x) inches by (11 - 2x) inches. The formula for volume is V = length × width × height. Since the height is equal to the side length of the square, the volume can be calculated by multiplying the three side lengths together: V = x(8.5 - 2x)(11 - 2x).
To find the maximum volume, we can take the derivative of V with respect to x, set it equal to 0, and solve for x. After solving, we find that x ≈ 1.18 inches. Plugging this value back into the formula, the maximum volume is approximately 28 square inches.