8. (a) Given 51 + 2 cos no neN show that 32 cos 0=cos 60+ 6 cos 40+ 15 cos 20+ 10 (5) R x x=4 Figure 2 Figure 1 Figure 1 shows a solid paperweight with a flat base. Figure 2 shows the curve with equation y=Hcos where H is a positive constant and x is in radians. -4x4 The region R, shown shaded in Figure 2, is bounded by the curve, the line with equation x=-4, the line with equation x = 4 and the x-axis. The paperweight is modelled by the solid of revolution formed when R is rotated 180 about the x-axis. Given that the maximum height of the paperweight is 2 cm, (b) write down the value of H. (1) (c) Using algebraic integration and the result in part (a), determine, in cm, the volume of the paperweight, according to the model. Give your answer to 2 decimal places. [Solutions based entirely on calculator technology are not acceptable.] (d) State a limitation of the model. (5) (1)