## Calculus Work Integration Problems

Hey, I need some help with a few word problems. Any help on them would be great, thanks.

1) A tank in the shape of an inverted right circular cone has height meters and radius meters. It is filled with 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

2) A trough is 8 meters long, 2.5 meters wide, and 3 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 3 meters, and base, on top, of length 2.5 meters). The trough is full of water (density ). Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use as the acceleration due to gravity.)

3) A circular swimming pool has a diameter of 10 m, the sides are 4 m high, and the depth of the water is 2.5 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 and the density of water is 1000 .)

Thanks!