page 07 MARKS 11. A manufacturer of chocolates is launching a new product in novelty shaped cardboard boxes. CHOCOLATES The box is a cuboid with a cuboid shaped tunnel through it. • The height of the box is h centimetres • The top of the box is a square of side 3x centimetres • The end of the tunnel is a square of side x centimetres • The volume of the box is 2000 cm3 h x 3x (a) Show that the total surface area, A cm2, of the box is given by 2 4000 16x A x = + . (b) To minimise the cost of production, the surface area, A, of the box should be as small as possible. Find the minimum value of A. [Turn over 3 6