Find the work done in pumping gasoline that weighs 46 pounds per cubic foot. ( H

Question

Find the work done in pumping gasoline that weighs 46 pounds per cubic foot. (Hint: Evaluate one integral by a geometric formula and the other by observing that the integrand is an odd function.)

A cylindrical gasoline tank 3 feet [ wavelength of the lowest UHF and highest VHF radio frequency, 300 MHz] in diameter and 4 feet long is carried on the back 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 contents of the fuel tank into the tractor. (Round your answer to three decimal places.)

Explanation / Answer

use the fact that the when you want to calculate the amount of work done lifting a mass, just multiply its weight times how far its CENTER OF GRAVITY was raised. This turns out to be equivalent to the integral. The old center of gravity was on the cylinder's axis, and all the mass got lifted to a point 6.5 feet above that. So the work done was:

Weight × 6.5 feet
= (46)**(1.5)^2*(4)* 6.5
= 2691

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