A reservoir is shaped like a straight circular cone, with the top pointing down (like an ice cream cone). Its height is 7 m, the radius of its circular upper face is 4 m, and it is filled with water to a height of 5 m. The purpose of this question is to determine the total work required to pump the entire amount of water to a height of 1 m above the top of the tank. Reminder: the density of water is = 1000 kg/m3 and the acceleration due to gravity at the surface of the earth is g = 9.8 m/s2. a) Let x 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 (x) of a thin layer of water between the heights x and x + x. To get all the points: - You must clearly draw and label your figure. - You must show all your work and briefly explain your answer. b) What is the approximate work W(x) required to pump the thin layer of water (described in part (a)) up to a height 1m above the top of the tank? Briefly justify your answer. c) Give a definite integral that calculates the total work required to pump all the water from the reservoir to a height of 1m above its top. Don't calculate the integral, just write it down