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

9. (10 points) A rectangular box L=6 ft, W =4 ft, and H = 5 ft is filled with water (pg = 62.5 lbs/ft3). H W a. If the origin of the coordinates (x, y, z) = (0, 0, 0) is at the front, bottom corner of the above figure, what are the coordinates of the centroid? b. How much work is done pumping the water to a point 3 feet higher than the top of the box? (similar to 5.4 #31-34) Use the method of centroids. 10. (10 points) A sphere of radius 4 feet is filled with water pg = 62.5 lbs/ft3 . How much work is done pumping the liquid to a point 2 ft above the top of the sphere? Hint: Put the origin of your x-y coordinates at the center of the sphere. If you have trouble with the integral, then use the same centroid method of problem #9 instead