MAT1322 IMAGE

Q13. A tank is shaped like a circular cone, with its apex pointing down {like an ice cream cone). Its height is 15 m, the radius of its top circular face is 4m, and it is lled with water to a height of 12m. 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 = 1000 kg,."m3 and the acceleration due to gravity on Earth's surface is g = 9.8 mfs2. (a) [3 points] Let :r 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 :1: and :r + Aa- m. To earn full marks: b You must draw and clearly label a diagram. D You must show all your work and briey explain your answer. (b) [1 point] What is the approximate work W(z) required to pump the thin layer of water (described in part (a)) to a height 1 m 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