A cylindrical tank has a radius of 3 m and a height of 7 m. The tank is filled with water. Find the work needed to pump the top 3 m of water out the top of the tank.

Answer 1

dW=force×distance

force=ρ⋅g⋅dV

The distance the water must be lifted is 7−y meters

dV=πr2⋅dy=π(32)⋅dy=9π⋅dy

So, the work required to lift that slice of water is:

dW=ρ⋅g⋅9π⋅(7−y)⋅dy

Total Work:

W=∫1000⋅(9.8⋅9π⋅(7−y))dy

solve the integration between 4 and 7

then:

W=396,900π