A cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. How much work is done in pumping a full tank of Water up to ground level? (The water weighs 9800 newtons per cubic meter.)
A) $548,800 \pi$ joules
B) $686,000 \pi$ joules
C) $411,600 \pi$ joules
D) $1,234,800 \pi$ joules
E) $1,029,000 \pi$ joules

Question

A cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. How much work is done in pumping a full tank of Water up to ground level? (The water weighs 9800 newtons per cubic meter.) 
A) $548,800 \pi$ joules
B) $686,000 \pi$ joules
C) $411,600 \pi$ joules
D) $1,234,800 \pi$ joules
E) $1,029,000 \pi$ joules

Quizplus · Accepted Answer

The volume of water in the tank is given by

$V = \pi r^2 h = \pi(2^2)(5) = 20\pi$ cubic meters

The weight of the water is given by

$W = V 	imes 9800 = 20\pi 	imes 9800$ Newtons

To raise this volume of water from a depth of 1 meter to ground level requires work equal to the weight of the water times the distance it is raised:

$W_	ext{total} = 9800 	imes g 	imes h_	ext{total} 	imes V = 9800 	imes 9.8 	imes 6 	imes 20\pi = 686,000\pi$ joules

Therefore, the answer is B.

A Cylindrical Water Tank 5 Meters High with a Radius 548,800π548,800 \pi548,800π

A Cylindrical Water Tank 5 Meters High with a Radius $548,800 \pi$