# Work Problem

• Mar 17th 2010, 06:44 PM
kaiser0792
Work Problem
Need some help guys!

A cylindrical water tank 12 feet high with a radius of 8 feet is buried so that the top of the tank is 3 feet below ground level. How much work is done in pumping a full tank of water up to ground level?

(weight of water is 62.4 pounds per cubic foot)

I set it up this way:

W = Integral (evaluated from 0 to 15) of (62.4)(pi)(64-y^2)(15-y)dy

I'm either incorrect in representing radius^2 as 64-y^2 which I derived from equation of an incremental disc of water having equation
x^2 + y^2 = 64 or in my limits of integration.
• Mar 17th 2010, 06:49 PM
skeeter
Quote:

Originally Posted by kaiser0792
Need some help guys!

A cylindrical water tank 12 feet high with a radius of 8 feet is buried so that the top of the tank is 3 feet below ground level. How much work is done in pumping a full tank of water up to ground level?

(weight of water is 62.4 pounds per cubic foot)

I set it up this way:

W = Integral (evaluated from 0 to 15) of (62.4)(pi)(64-y^2)(15-y)dy

I'm either incorrect in representing radius^2 as 64-y^2 which I derived from equation of an incremental disc of water having equation
x^2 + y^2 = 64 or in my limits of integration.

the radius of the tank is a constant ...

$W = \int_0^{12} 62.4(64\pi)(15-y) \, dy$
• Mar 17th 2010, 06:52 PM
kaiser0792
Thanks Skeeter, your a big help!