A tank has the shape of a straight circular cone 9 m high and 4 m radius, with the tip at the bottom. It is filled with water up to a height of 8m. The purpose of this issue is the total work necessary to pump all the water to a height of 2m above the top of the tank. We give the density of water o = 1000 kg/m' and gravitational acceleration G = 9.8 M/s?. Let z in meter the height measured from the bottom of the tank. (A) (3 points] Find an expression in fouction of a for the approximate volume AV (x) of a thin layer of water between heights a and a + Ar. Brief justification for your answer. A figure could help explain your answer. Let S be the solid of revolution obtained by rotation of the axis mitour region We consider the circle obtained by the perpendicular section of the solid S at position o. To find you. rouverane con R(z) A(Z) = (C) (3 points] Give an improper integral that cales the volume of S and determine whether it converges or diverges. If it converges, find the exact volume of S . Your answer must be well justified and Use the appropriate mathematical notation. Show all the details of your work