# Emptying a Tank of Beer

1. Oct 27, 2013

### eumyang

So a cousin has asked me for Calculus help, but my Calculus is rusty. She's in Calculus II (of a 3-semester sequence in the US) and is on Work. I decided to make up a problem for her, but I want to make sure I know what I'm doing.

1. The problem statement, all variables and given/known data
A cylindrical tank (16 feet high with a radius of 4 feet) is half full of beer that weighs 63 pounds per cubic foot. Find the work requred to pump beer out through a spout in the top of the tank.

2. Relevant equations
$W = {\int_a}^b F(x) dx$

3. The attempt at a solution
I just would like to know if I had set up the integral right.

The volume of a disk of beer would be $\pi \cdot 4^2 \Delta\ y$
The weight of a disk of beer would be $63 \cdot 16\pi \Delta y = 1008\pi \Delta y$
The distance to move a disk of beer to the top would be $16 - y$

$W = {\int_0}^8 1008\pi (16 - y) dy$
Is the integral this? Seems too simple. If so, I can take it from here.

2. Oct 27, 2013

### Office_Shredder

Staff Emeritus
That looks good to me.

3. Oct 27, 2013

### eumyang

Whew! Glad I'm not totally out of it. Thanks.