A rectangular box with no top is to be constructed from a 10 in. x 10 in square piece of cardboard by cutting equal square of side x from each corner and then bending up the sides. Write the volume of the box as a function of x.

Answer 1

let the side of the cut-out square be x inches

base is 10-2x by 10-2x, and the height is x

Volume = x(10-2x)^2 , where x > 5 , or else the base is negative.