b). A manufacturer makes a metal cone to hold concrete. The volume enclosed by the cone is determined by rotating the line y = 2x + 2.4 around the x - axis between x = 0 and x = 10. Calculate the volume of concrete which it can hold. y = 2x + 2.4 X-axis 0 10 Figure 3 Metal cone 14 a) An open rectangular water tank with square ends is to be made from a thin sheet of metal. () What is the least area of metal for which the volume is 14 m3? (ii) Use the second order derivative to show that this is a minimum b) The height of a road surface H (in metres) above a datum is given by the equation :- H = - 0.1 x2 + 0.48x - 0.06 Where 'x' is the distance from the datum. (a) Calculate the maximum height of the road above the datum. (b) Determine the second order derivative and use it to show that the turning point is a maximum