A cylindrical gasoline tank 4 feet in diameter and 4 feet long is carried on the bank of a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank Is 5 feet above the top of the tank in the truck. Find the work done in pumping the entire gasoline
Contents that weighs 42 pounds per cubic feet of the fuel tank into a tractor. (Hint: Evaluate one Integral by geometric formula and the other by observing that the integrand is an odd function.)

Question

Quizplus · Accepted Answer

The work done in pumping the gasoline can be calculated by considering the weight of the gasoline (42 pounds per cubic foot) and the distance it needs to be lifted (5 feet above the tank, plus the radius of the tank to reach the bottom when starting, which is 2 feet, totaling 7 feet). The volume of the cylindrical tank is given by $V = \pi r^2 h$, where $r = 2$ feet and $h = 4$ feet, so $V = \pi \cdot 2^2 \cdot 4 = 16\pi$ cubic feet. The work done is $W = \text{weight} \times \text{distance} \times \text{volume} = 42 \times 7 \times 16\pi = 4,704 \pi \, \text{ft-lb}$.

A Cylindrical Gasoline Tank 4 Feet in Diameter and 4 9,408πft−lb9,408 \pi \mathrm { ft } - \mathrm { lb }9,408πft−lb

A Cylindrical Gasoline Tank 4 Feet in Diameter and 4 $9,408 \pi \mathrm { ft } - \mathrm { lb }$