NAME: MATH 152 February 11, 2016 QUIZ 3 • Show all your work and indicate your final answer clearly. You will be graded not merely on the final answer, but also on the work leading up to it. • You may not use your class notes, calculator, cell phone, or any other electronic devices. 1. (6 points) Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y = x2 , y = 0, x = 1, and x = 2 about x = 4. 2. (6 points) A force of 20 lbs is required to hold a spring stretched 4in. beyond its natural length. How much work W is done in stretching the spring from its natural length to 8 in. beyond its natural length? NAME: MATH 152 February 11, 2016 3. (6 points) The aquarium shown below is full of water. Find the work needed to pump all of the water out of the aquarium. Use 62.5 lb/ft3 for the weight density of water. Assume that a = 3 ft, b = 2 ft, c = 6 ft, and d = 1 ft. You may write your answer as a multiple of 62.5 without multiplying it out.