Problem 1. (1 point) Problem 3. (1 point) The design of boats is based on Archimedes' Principle, which On paper, sketch the solid obtained by rotating the region bounded states that the buoyant force on an object in water is equal to the by y= x', x = 1, and y = -1 around the axis y = -1. Using the weight of the water displaced. Suppose you want to build a sail- sketch, write a Riemann sum approximationg the solid (use Dx for boat whose hull is parabolic with cross section y = ax, where a Ar): is a constant. Your boat will have length L and its maximum draft volume # E (the maximum vertical depth of any point of the boat beneath the water line) will be H. See the figure below. Then convert your sum to an integral and find the volume. volume = Answer(s) submitted: (incorrect) Problem 4. (1 point) (Click on the figure for a larger version.) Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y = x, y = 1, and the y-axis about the Every cubic meter of water weighs 10# newtons. What is the max- line y = -3. imum possible weight for your boat and cargo? Volume = weight = newtons Answer(s) submitted: Answer(s) submitred: (incorrect) (incorrect) Problem 2. (1 point) Problem 5. (1 point) Find the volume of the solid whose base is the region in the first Find the volume of the solid whose base is the region in the first quadrant bounded by y = x, y = 1, and the y-axis and whose quadrant bounded by y = x, y = 1, and the y-axis and whose cross-sections perpendicular to the x axis are semicircles. cross-sections perpendicular to the x axis are squares. Volume = Volume = Answer(s) submitred: Answer(s) submitted: (incorrect) (incorrect)