Question

The region consisting of all points in three-dimensional space within 3 units of line segment ab has a volume 216 pi. what is the length ab

Answer 1

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.