A vertical right circular cylindrical tank measures 26 ft high and 12 ft in diameter. It is full of oil weighing 60 lb ft3.

Question

A vertical right circular cylindrical tank measures 26 ft high and 12 ft in diameter. It is full of oil weighing 60 lb ft3. How much work does it take to pump the oil to the level of the top of the tank? Give your answer to the nearest ft-lb.

1. 9,174,456 ft-lb
2. 38,227 ft-lb
3. 2,293,614 ft-lb
4. 4,587,228 ft-lb

Answer 1

Slice the cylinder into very thin circles of depth dy and area pi*r^2 (each slice has a volume = dy*pi*r^2). Density times that volume = either lbs force or lbs mass (depending on the units of density - normally in math problems like this, density is given in lbs force per cu ft). Work = that force times the distance to move it to the top of the tank. Integrate from the bottom to the top of the tank to add all the small pieces of work together. The final integral should be the integral from 0 to 26 of (60*6^2*pi*(26-y)dy which turns out to be answer 3 (2.3 million ft lbs)