find how much work it takes to empty a full hemispherical water reservoir of radius 5m by pumping the water to a height of 4 m above the top of the reservoir. water weighs 9800 N/m^3.
I need to find the volume first so i think it's v=integral (pi*r^2)
so V = pi * integral (25-y^2) dy from 0 to 5
which is 250*pi/3
mass = density * volume = 9800n/m^3 * 250*pi/3 = 2.45*10^6*pi / 3
force = mass * 9.8m/s^2 (gravity) = 2.401*pi*10^7 /3
then work = force*x = [2.401*pi*10^7 /3] *4m
am i doing this right?