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. B) 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) 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