<h3>Answer:</h3>
- x = 5/6 in ≈ 0.83 in
- v = 125/108 in³ ≈ 1.16 in³
The width of the cardboard (in inches) will be 4x, and its length will be (5-4x) so the perimeter adds up to 10 in. Then the volume is the product of the area of the open ends (x²) and the length (5-4x).
The graphing calculator shows that volume is maximized when the value of x is 0.833, or 5/6 inch. The corresponding length is 5-4x = 5/3 inch, so the volume is ...
... v = (5/6)²×(5/3) = 125/108 . . . . in³
The corresponding decimal values of x and volume are ...
... x ≈ 0.83 in
... v ≈ 1.16 in³