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1. Let R be the region inside the curves y = 0, x = 0, y...

1. Let R be the region inside the curves y = 0, x = 0, y = 6, and y = 2x − 4. A water tank is in the shape of the region R rotated about the y axis. If the water tank is filled up to a height of y = 5 meters, find the work required to pump the water to a platform 5 meters above the top of the tank. Use ρg = 9800.

2. A submarine dives under the surface of the ocean. A side of the submarine is in the shape of a disk of radius 4 meters. If the top of the submarine is 200 meters below the ocean’s surface, calculate the force due to hydrostatic pressure on this side of the submarine.

Hint: This is similar to a tank filled with water except the water is pushing into the submarine from the outside instead of pushing towards the outside from within the submarine. Another difference is that the water level is above the submarine. However, you may still use the same formula and approach that we used in class to find the force on this circular side. Hint 2: Place the center of the disk at the origin (0, 0). The surface of the water is 200 meters above the top of the disk.

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