i need help with these questions. they are all similar, but i dont know how to approach them. i have no clue how to do them.
1. A trough is 3 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^2 from x=-1 to x=1. The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot.
2. A tank in the shape of an inverted right circular cone has height 8 meters and radius 10 meters. It is filled with 1 meters of hot chocolate.
Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. Note: the density of hot chocolate is 1460 kg/m^3.
3. A trough is 5 meters long, 1 meters wide, and 2 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 2 meters, and base, on top, of length 1 meters). The trough is full of water (density 1000 kg/m^3). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use 9.8 m/s^2 as the acceleration due to gravity.)
4. A circular swimming pool has a diameter of 20 m, the sides are 3 m high, and the depth of the water is 1.5 m. How much work (in Joules) is required to pump all of the water over the side? (The acceleration due to gravity is 9.8 m/s^2 and the density of water is 1000 kg/m^3.)