Answer
The required volume of water is $1300~m^3$.
Work Step by Step
The power output is 2000 MW, which is $2.0\times 10^9~W$
92% of the work done by gravity on the water is converted to electricity.
$0.92~Work = (2.0\times 10^9~W)(1~s)$
$Work = 2.17\times 10^9~J$
The work done by gravity on the water is $mgh$.
$mgh = 2.17\times 10^9~J$
$m = \frac{2.17\times 10^9~J}{gh}$
$m = \frac{2.17\times 10^9~J}{(9.80~m/s^2)(170~m)}$
$m = 1.3\times 10^6~kg$
We can find the volume $V$ of water in cubic meters.
$V = \frac{1.3\times 10^6~kg}{1000~kg/m^3} = 1300~m^3$
The required volume of water is $1300~m^3$.
