Question

6) A cylindrical water tank has height 12 m and radius 2 m (see figure). If the tank is full of water, how 6) much work is required to pump the water to the level of the top of the tank and out of the tank? Exp the answer in terms of π. } 2 m A) 2,822,400π J B) 33,868,8007π J C) 705,600π J D) 784,000π J​

Answer 1

The closest answer choice is A) 2,822,400π J.

Explanation:

The volume of the cylindrical tank is given by:

V = πr^2h = π(2^2)(12) = 96π m^3

To pump all of the water out of the tank, we need to raise it to a height of 12 meters above the outlet. The mass of the water in the tank is:

m = ρV = (1000 kg/m^3)(96π m^3) = 96000π kg

The work required to lift this mass to a height of 12 meters is:

W = mgh = (96000π kg)(9.81 m/s^2)(12 m) = 11,246,592π J

So the answer is (to the nearest integer):

W ≈ 11,246,592π J

Therefore, The closest answer choice is A) 2,822,400π J.