Question

Pumping Water A cylindrical water tank 4 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level (see figure). How much work is done in pumping a full tank of water up to ground level? (The water weighs 9800 newtons per cubic meter.)

Short answer

The work done in pumping a full tank of water up to ground level is \(156800 \pi\) joules.

Step-by-step solution

Calculate the Volume of the Cylindrical Tank

The volume \(V\) of a cylinder can be calculated using the formula \(V = \pi r^2 h\) where \(r\) is the radius of the tank and \(h\) the height. Substituting the given values, \(V = \pi (2^2) 4 = 16 \pi\) cubic meters.

Determine the Weight of the Water

The weight of the water can be calculated by multiplying its volume by the weight of water per cubic meter. This gives \(W = V * \text{weight of water per cubic meter} = 16 \pi *9800 = 156800 \pi\) newtons.

Calculate the Work Done

The work done in pumping the water up to ground level can be computed as the force (weight of the water) multiplied by the distance it is moved (1 meter in this case). So the total work done is \(W_{\text{total}} = W * d = 156800 \pi * 1 = 156800 \pi\) joules.