Q13. A tank is shaped like a circular cone1 with its apex pointing down {like an ice cream cone}. Its height is 7m1 the radius of its top circular face is 4m, and it is lled with water to a height of 5 m. The goal of this question is to determine the total work required to pump all of its water to a height 1m above the top of the tank. Recall: the density of water is p = 1300 kgfn'i3 and the acceleration due to gravity on Earth's surface is g = 9.3 mfsz. {a} [3 points] Let I be the height (in m) measured from the bottom of the tank (the tip of the cone). Find an expression for the approximate volume V{;r) of a thin layer of water between heights I and I + r: m. To earn full marks: I'- You must draw and clearly label a diagram. II- 1tlrou must show all your work and briey explain your answer. {b} [1 point] What is the approximate work W[I) required to pump the thin layer of water {described in part {an to a height 1m above the top of the tank? Briey justify your answer. (c) [1 point] Give a denite integral that computes the total work required to pump all of the water in the tank to a height of 1m above its top. Do not evaluate the integral just write it down