question_answer 80)

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

Answer:

Let x cm be the side of the square to be cut from from corner at the given square piece of tin of side 18cm.       Therefore the box.       l = 18 ? 2x cm. b = 18 ? 2x cm.       and h = x cm        Volume of the box        V = lbh = (18 ? 2x)2x       = (324 + 4x2 ? 72x) x                                     but x = 9  which is impossible        x = 3       Now       = V is maximum when x = 3       Hence volume of the box will be maximum when the side of the square to be cut from each corner = 3 cm.