Volume of the region V = 216 pi
The region is three dimensional with 3 unit line segment, therefore r = 3
From the given text, we have we have a cylinder with two hemispheres.
So the volume V = volume of our cylinder + volume of our two hemispheres
Volume of 2 hemispheres = (2pi/3) r^3 + (2pi/3) r^3 = (4pi/3) r^3
Volume of cylinder = pi r^2 h
So 216 pi = (4pi/3) r^3 + pi r^2 h => 216 = (4/3)3^3 + 3^2 h => 216 = 36 + 9h
=> 9h = 180 => h = 20
So the length AB = 20.
