An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

A square piece of tin of side 18 cm is to be made into a box without top, by cutting off square from each corner and foling up the flaps of the box. What should be the side of the square to be cut off so that the volume of the box is maximum possible.

A rectangular sheet of tin 45 cm by 24 cm is to made into a box without top, by cutting-off square from each other corner and folding up the flaps. What should be the side of the square to be cut-off so that the volume of the box is maximum?