3 A water tank, shown to the right, is shaped like an inverted cone with height 4 m and base radius 1 m. a. If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank? Use 1000 kg/m for the density of water and 9.8 m/s for the acceleration due to gravity. b. Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full? Explain. a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the bottom of the tank as the origin. For 0 sys4, find the cross-sectional area A(y) in terms of y. 16 2 A(y)=1000x -h (Simplify your answer. Type an exact answer, using x as needed. Use integers or fractions for any numbers in the expression.) 4 m