# Thread: Calculus 2 Applications to physics Cylindrical Problem

1. ## Calculus 2 Applications to physics Cylindrical Problem

A vertical right circular cylindrical tank measures 24 ft high and 12 ft in diameter. It is full of oil weighing 60lb/ft3. How much does it take to pump the oil to a level 2 ft above the top of the tank? Give your answer to the nearest ft lb.

2. Originally Posted by Collegeboy110
A vertical right circular cylindrical tank measures 24 ft high and 12 ft in diameter. It is full of oil weighing 60lb/ft3. How much does it take to pump the oil to a level 2 ft above the top of the tank? Give your answer to the nearest ft lb.
So work is equal to Force times Distance

First we need to find the volume of a little slice(they are little cylinders)

$dV=\pi (6)^2dx$ this is in cubic feet. To convert this to a force use the above to get

$dF=60\cdot \pi (6)^2dx=2160\pi dx$

We know that we have to move each slice x+2 feet so ...

$\int_{0}^{24}(x+2)2160\pi dx=2160 \pi \int_{0}^{24}(x+2) dx$

3. Makes sense, so to finish the problem you will just integrate and plug in 24 and 2? and would it be from 24 to 2 because it wants it to be " 2ft above the tank?"

4. Originally Posted by Collegeboy110
Makes sense, so to finish the problem you will just integrate and plug in 24 and 2? and would it be from 24 to 2 because it wants it to be " 2ft above the tank?"
Not quite the x+2 is the distance moved so we only need to integrate from 0 to 24.

for instance the slice on top at x=0 only moves 0+2ft=2ft

The very bottom slice moves 24+2=26ft.

I hope this helps. Good luck.

5. I got 725,760(pi) is this correct?