# Math Help - work with cylindrical tank

1. ## work with cylindrical tank

A right cylindrical tank is filled with sea water. The tank has a radius of 6 feet and a height of 12 feet. If the water level is now 3 feet below the top of the tank, how much work will be required to pump the sea water to the top of the tank? (The weight-density of seawater is 64 lb/ft^3)

I have

r=6 ft, and h=12ft
so far my equation is like this
W= pi (6)^2 (64)y

2. See attachment

For a general discussion of tank problems you might want to check out

Work

3. Originally Posted by linlinrocks
A right cylindrical tank is filled with sea water. The tank has a radius of 6 feet and a height of 12 feet. If the water level is now 3 feet below the top of the tank, how much work will be required to pump the sea water to the top of the tank? (The weight-density of seawater is 64 lb/ft^3)

I have

r=6 ft, and h=12ft
so far my equation is like this
W= pi (6)^2 (64)y
work = $\int WALT$

W = weight density
A = cross-sectional area of a representative horizontal "slice" of liquid (in terms of y if variable)
L = amount of lift in terms of y for a representative horizontal "slice" of liquid
T = "slice" thickness ... dy

work = $\int_0^9 64 \cdot 36\pi \cdot (12-y) \, dy$