question_answer 1)

A rectangular sheet of tin 45 cm × 24 cm. is to be made into a box without top, by cutting off square from each 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 ? 

Answer:

Let x cm. be the side of the square to be cut                             l = (45 ? 2x) cm       b = (24 ? 2x) cm and h = x cm       Volume (V) of the box = lbh       V = (45 ? 2x) (24 ? 2x) x       = 4x3 ? 138x3 + 1080 x       = 2 [2x3 ? 69x2 + 540x]             = 12 [x2 ? 23x + 90]                         Now                     is maximum when x = 5. Here volume of box will be maximum when side of the s square to be cut = 5 cm.