l -> ( T.r' + \"Um + Hll] '[J'l . 'f ' lllii' gm 1.1m:- 0.2:] The graph above shows two functions, f(x) and g(x). The function f(x) is a polynomial that has been generated to fit through the points A, B and C shown below. The area bounded by the curves f(x) and g(x) and the lines x = 0 and x = 7.5 is to be rotated by 360 about the x-axis to form a solid of revolution which is to be used as a design for a drinking vessel. 5 . Calculate the x-intercept for g(x) {1 mark} Calculate the area between the curves f(x) and 90:), bounded by the lines x 0 and x = 7.5 (2 marks) Show that the maximum volume of liquid the vessel can contain is approximately 101.3 units3. (smarks) By calculating the volume ofthe solid of revolution created by rotating the area bounded by the curves f(x) and 9(x) and the lines x = 0 and x = 7.5 by 360, find the volume of material required to construct the drinking vessel. {3 marks) . If the drinking vessel is partly filled to contain 80 units3 of water, calculate the depth of water in the drinking vessel