A cylindrical tank, shown to the right, has height 8 m and radius 5 m. a. If the tank is full of water, how much work is required to pump the water to the level of the top of the tank and out of the...

Extracted text: A cylindrical tank, shown to the right, has height 8 m and radius 5 m. a. If the tank is full of water, 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 the water out of the tank when it is half full as when it is full? Explain. 8 m 5m a. Draw a y-axis in the vertical direction (parallel to gravity) and choose the center of the bottom of the tank as the origin. For 0sys8, find the cross-sectional area A(y). A(y) = |(Type an exact answer, using t as needed.) Set up the integral that gives the work required to pump the water out of the tank. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using z as needed.) O A. dx O B. The amount of work required is approximately (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.) b. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes. It takes exactly half as much work to pump the water out of the tank when it is half full. B. No. The amount of work required to pump the water out of the tank when it is half full is approximately J. (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.)