Question

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box can be made. if the cardboard is 13 in. long and 6 in. wide and the square cutaways have dimensions of x in. by x in., find a function giving the volume v(x) of the resulting box.

Answer 1

try sketching the cardboard piece labeling each side. when folded, the height of the box is x, the length is now (13 - 2x), the width is now (6 - 2x) after cutting out the squares from each corner.

volume = length*width*height

V(x) = x(13 - 2x)(6 - 2x)