Please show all work, step by step. Thank you so much!

5. (10 points) 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=2 feet above the top of the tank? pg = 62.4 lbs/ft3. Note: Define your coordinate system with its origin corresponding to the center of the sphere so that x2 + y? = 52. r a. What is h2? b. What is h1? c. If h(y) = H - y, then what is H? d. What is d(vol) = A(x) dy? 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)