• 1. Find the centroid of the figure bounded by x = (y+2)² and x = 5
  • Make a graph of the figure.
  • Compute M
  • Compute M_y
  • Compute x_c(the x centroid)
  • Compute M_x
  • Compute y_c (the y centroid)
  • Draw your centroid on a plot with the triangle. Attach a screenshot.
  • Does it look like the center of gravity of the figure? (yes or no)
• 2. A rectangular box L= 6 ft, W = 4 ft, and H = 5 ft is filled with water (rg = 62.5 lbs/ft³). 1. 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? 2. 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.
• 3. A sphere of radius 4 feet is filled with water pg = 62.5 lbs / ft^3 . 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.

radius = 4 ft