A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures $4$ inches by $10$ inches. Six squares will be cut from the cardboard: one square will be cut from each of the corners, and one square will be cut from the middle of each of the $10-$inch sides. $($See Figure $1.)$ The remaining cardboard will be folded to form the box and its lid. $($See Figure $2.)$ Letting $x$ represent the side$-$lengths $($in inches$)$ of the squares, use the ALEKS graphing calculator to find the value of $x$ that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.

Value of $x$ that maximizes volume: $$ in

Maximum volume: $$ in ${?}^3$