A water tank is shaped like an inverted cone with height 6 m and base radius 1.5 m
If the tank is full, how much work is required to pump the water to the level of the top of the tank and out of the tank?
Integral of ( density * g (acceleration due to gravity) * A(y) (area of a cross section ) * change in y )
The Attempt at a Solution
The integral is from zero to 6 since this strange cone-shaped tank is 6 m high. g = 9.8 m/s^2, times the change in y which is (y-6) since the cone is 6m high
My problem is that I have no idea how to compute the cross-sectional area of a cone. The cuts are circles which have an area of pi*r^2. The tricky thing with this problem though is the radius does not remain constant from top to bottom.
My solutions manual gives the area as pi * (y^2)/16. I have no idea how they got to this. Any help would be very much appreciated.