Missing data in the problem:
"..the United States produced
of electrical energy.."
a) 77.8 kW
Here we are given the total energy produced by the 4138 power plants. In fact, the total energy produced is

And converting into Joules:

We know that this energy has been produced by
n = 4138
power plants, so the average energy produced by each power plant in 1 year was

The time in 1 year is:

So, the average power output of each power plant was

b)

We said that the energy output of each power plant in 1 year is

But we also know that each plant is 90% efficient, so the actual initial mechanical energy due to the volume of water in the dam is

This is the amount of energy stored in the water in each dam. As the water falls down, the initial gravitational potential enegy is converted into electrical energy. The initial gravitational potential energy of hte water is

where
m is the mass of the water
is the acceleration of gravity
h = 50.0 m is the height of the water
Solving for m,

And since the density of water is

The total volume of water in each dam was
