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.
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)
$\displaystyle dV=\pi (6)^2dx$ this is in cubic feet. To convert this to a force use the above to get
$\displaystyle dF=60\cdot \pi (6)^2dx=2160\pi dx$
We know that we have to move each slice x+2 feet so ...
$\displaystyle \int_{0}^{24}(x+2)2160\pi dx=2160 \pi \int_{0}^{24}(x+2) dx$