Final answer:
The volume of the box formed from cardboard by cutting out squares from each corner and folding up the sides is calculated by the formula V = (10 - 2x) × (12 - 2x) × x, where x is the side length of the squares cut out.
Step-by-step explanation:
To find the volume of the box created from a sheet of cardboard with squares cut out from each corner, we need to subtract the length of the squares, x inches, from each dimension of the cardboard. After folding the sides up, the dimensions of the box will be (10 - 2x) inches in length, (12 - 2x) inches in width, and x inches in height, since the height of the box corresponds to the side length of the squares we cut out.
Therefore, the volume of the box, V, is given by:
V = length × width × height
V = (10 - 2x) × (12 - 2x) × x
To find the volume, one would simply substitute the value of x (the side length of the squares being cut out) into the equation and solve.