$(6$ points$)$ A large wind turbine is used for electricity generation. The turbine has a blade span diameter of $47$ m and is installed in an area that has steady winds at $3\mathrm{.}9\frac{m}{s}.$ This wind

turbine$-$generator converts $28\mathrm{.}4\%$ of the available energy into electricity. The density of the air is $1\mathrm{.}25\frac{kg}{m^3}.$

$($Hint: Think of the air as flowing through a pipe that has a diamter similar to the wind turbine. Wind turbines take advantage of the air's velocity.$)$

What is the power generated from this windmill?

If the blade span diameter is reduced by $30\%,$ the efficiency of the turbine$-$generator increases to $59\mathrm{.}356\%.$ What is the power generated from this new design.