Content attribution Question An open-top box is to be made from a 20 in by 30 in piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What is the maximum possible volume of the box? Round your answer to the nearest whole number and omit units from the answer box. Provide your answer below:

Step 1 ：Let the side length of the squares that are cut out from the corners be denoted as \(x\).

Step 2 ：The length of the box will be \(30 - 2x\), the width will be \(20 - 2x\), and the height will be \(x\).

Step 3 ：The volume \(V\) of the box can be expressed as \(V = x(30 - 2x)(20 - 2x)\).

Step 4 ：To find the maximum volume, we need to find the maximum of this function. This can be done by taking the derivative of the function, setting it equal to zero, and solving for \(x\).

Step 5 ：The derivative of the volume function is \(-2x(20 - 2x) - 2x(30 - 2x) + (20 - 2x)(30 - 2x)\).

Step 6 ：The critical points of the function are \(\frac{25}{3} - \frac{5\sqrt{7}}{3}\) and \(\frac{5\sqrt{7}}{3} + \frac{25}{3}\).

Step 7 ：Substitute these values of \(x\) back into the volume function to find the maximum volume.

Step 8 ：The maximum volume is \(\left(\frac{10}{3} + \frac{10\sqrt{7}}{3}\right)\left(\frac{25}{3} - \frac{5\sqrt{7}}{3}\right)\left(\frac{10\sqrt{7}}{3} + \frac{40}{3}\right)\).

Step 9 ：The maximum possible volume of the box, rounded to the nearest whole number, is \(\boxed{1000}\).