A spherical tank of radius 5 feet has its bottom half filled with water. How much work is done pumping the water to a point h=3 feet above the top of the tank? pg = 62.4 1bs/ft . Note: Define your coordinate system with its origin corresponding to the center of the sphere so that x- + y? = 42 r a. What is h2? b. What is hl? c. If h(y) = H - y, then what is H? d. What is d(vol) = A(x) dyf? e. Compute : W = , pg d(vol) h(y) f. Check your answer with using a Simpson's rule calculator. Attach a screen shot. g. Do your answers from (a) and (b) match? (yes or no) h. Check your answer by using the method of centroids (i.e. concentrating all the weight of the sphere at the center and moving the center to H. i. Do your answers from (a), (b), and (c) match? (yes or no)