For my calc 2 class, we are learning how to use integrals to find the work needed to do something. I under stand that the work of everything is the integral of the work of a slice.
I also understand that W=Force*distance. However in the problems that I am given, Force is variable. I know that F=mass*acceleration and that m=Density*volume. The acceleration is 9.8 due to gravity, density is usually given, and distance is usually top-the height of the slice. However I don't understand the volume part. I don't know what I am supposed to take the volume of and whether or not it is a constant.
The questions I have to complete are
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 9 meters long, 2 meters wide, and 5 meters deep. The vertical cross-section of the trough parallel to an end is shaped like an isoceles triangle (with height 5 meters, and base, on top, of length 2 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)...
4)...
5) ...
6)...
I know that this is alot of questions but if someone can help me of getting the concept of setting up the integral correctly, it would be greatly appreciated.