Part I 1. Using the method of integration, show that the volume of a right circular cone of altitude 'h' and base radius "a' units. 2. A tank is in the shape of an inverted cone, with height 10 ft and base radius 6 ft. The tank is filled to a depth of 8 ft to start with, and water is pumped over the upper edge of the tank until 3 ft of water remain in the tank. How much work is required to pump out that amount of water? 3. Find the centroid of the region with the indicated boundaries. a. The parabola y = 4 - x and the x-axis. b. The curves y = x2 - 4 and y = 2x - x2 c. Prove that the distance from the centroid of a triangle to any side of the triangle is equal to one -third the length of the altitude to that side