Caluculus Question

Question

A pool in the shape of a hemisphere with a radius of 7 feet is filled with 6 feet of water.  Letting   be the distance from the bottom of the hemisphere, set up the integral that would be used to find the total amount of work done in pumping the water to a point 5 fet above the top of the pool.  

Answer 1

dWork = dM g (12- y) { 12 is 7 + 5}

dM = ρ π ( 14 y - y² ) (where ρ is the density of water in kg /ft³ )

Work = π ρ g ∫ (12 -y) (14 y - y² ) dy { limits 0 to 6 }