Consider a cylindrical tank with radius R meters, length L meters, and filled with crude oil to a height of h meters (shown below). Assume the density of the oil in the tank is 870 kg/m3 and that the tank is on Earth, where the acceleration due to gravity is 9.8 m/s' 2R a. Find a formula for the volume of a generic "slice" of oil at depth y (you need to determine how y will be oriented). b. Turn this volume formula into a "force" formula by converting volume (m2) into mass (kg) and mass into force (kg-m/s, i.e. Newtons). c. Write a formula for the "work" required to pump each slice of oil out of the top of the tank. d. Finally, set up and evaluate an integral that gives the total work required to pump the oil out of the tank (it will be in terms of R, L, and h).