# 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?

##### 1 Answer

Jul 12, 2016

#### Explanation:

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