5.2. Volumes http://www.ck12.org

What is the volume of the solid generated when the region enclosed byy=√x,y= 3 ,andx=0 is revolved about
they−axis?
Solution:
Since the solid generated is revolved about they−axis (Figures 12a and 12b), we must rewritey=√xasx=y^2.
Thusu(y) =y^2 .The volume is

V=

∫d

c π[u(y)]

(^2) dy

∫ 3
0 π[y
(^2) ] (^2) dy

∫ 3
0 πy
(^4) dx
=π
[y 5
5

] 3

0

=π

[ 35

5 −^0

]

=^2435 π.

Figure 12a