Answer
$90$ horsepower
Work Step by Step
Let $h$ be the horsepower.
Let $r$ be the number of revolutions per minute.
Let $d$ be the diameter of the shaft.
$h=krd^3$
$h=40; r=120; d=2$
$40=k(120)(2)^3$
$k=\frac{1}{24}$
$h=\frac{1}{24}rd^3$
$r=80; d=3$
$h=\frac{1}{24}(80)(3)^3$
$h=90$ horsepower
