A right circular cylindrical water tank with height 5 meters and radius 2 meters is filled with water with density 1000 kg per cubic meter, which is 3 meters deep. The work done, in kg-meters, to remove the water from the tank is

A) $436,200 \pi$
B) $432,200 \pi$
C) $418,400 \pi$
D) $411,600 \pi$
E) $402,600 \pi$

Question

A right circular cylindrical water tank with height 5 meters and radius 2 meters is filled with water with density 1000 kg per cubic meter, which is 3 meters deep. The work done, in kg-meters, to remove the water from the tank is

A) $436,200 \pi$
B) $432,200 \pi$
C) $418,400 \pi$
D) $411,600 \pi$
E) $402,600 \pi$

Quizplus · Accepted Answer

The work done to remove the water is calculated by integrating the weight of each infinitesimal layer of water times the distance it needs to be lifted. The work is given by $ W = \int_0^3 \pi r^2 \rho g (h) \, dh $, where $ r = 2 $, $ \rho = 1000 $, $ g = 9.8 $, and $ h $ is the height from which the water is lifted. Solving this integral gives the work done as $ 411,600 \pi $ kg-meters.

A Right Circular Cylindrical Water Tank with Height 5 Meters 436,200π436,200 \pi436,200π

A Right Circular Cylindrical Water Tank with Height 5 Meters $436,200 \pi$