How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #x=sqrt(y)#, x=0, y=4 about the x-axis?
The ends of this first-quadrant segment of the parabola
(0, 0) and (2, 4).
The shell has a paraboloid-hole in the middle. The base is circular,
with radius ( range of y ) 4 units and the height is ( range of x, from 0
to 2 ) 2 units.
The hole volume has to be subtracted from the volume
of a right circular cylinder, of radius 4 and height 2 units..
So, the volume of the hollow solid =
the limits, from x = 0 to x = 2