What is the Riemann Sum and the integral to model the work that is required to pump the water to the level of the top of a tank that is an inverted cone shape with a height 2 meters and a top radius of 6 meters full of water?

Please explain steps in details: Density of water is approximately 1000 kg/m^3 and gravity is 9.81 m/s^2 . The function y = x^2 from x = 0 to 2 is rotated about the y-axis. 1) Find the volume of the resulting solid 2) If the resulting solid is filled with water, find the work done in emptying it - assume all units of measurement are in meters. Do we subtract? 3) Find the surface area of the resulting shape (set up the integral, and find a numerical approximation)

A reservoir shaped as a right-circular cylinder with a diameter of 40 meters and a height of 6meters is half full of water. Use an integral to find the work required to pump the water to alevel 2 meters above the top of the reservoir. Assume that water weighs 1000 kg/m3.

A vertical right circular cylindrical tank measures 21 feet high and has a 10 foot diameter. It is full of oil weighing 61.7 lb ft 3. a) Set up the work integral [clean up to just before integrating] showing how much work (in ft-lb) it takes to pump the oil to the level of the top of the tank (to empty the tank). b) Evaluate the answer from part a. Round your answer to the nearest whole ft-lb.