Volume using The Shell Method
Dec 31, 2015
Volume using The Shell Method
The shell method is like the washer method only the rotation is about the y-axis.
http://www.rkm.com.au/animations/animation-solid-revolution-2.html
If we take a vertical slice and revolve it about the y-axis we get cylinders. Then we add up the volume of all the cylinders
Sum of the cylindrical shells
Volume = ∑circumference ∙ height ∙thickness
n
dxhrn
v1
2lim
One Function:
The volume of the solid obtained by revolving R about the y-axis using cylindrical shells is given by:
b
a
dxxfxV )(2
1. Find the volume of the solid obtained by revolving f(x) about the y-axis if
4024)( 2 xforxxf
Two Functions:
The volume of the solid of revolution of the region bounded by f(x) and g(x) is given by:
b
a
dxxgxfxV )()(2
2. Find the volume of the revolution of the region bounded by the curves
axisyandxyandxy 422
3. Find the volume of the solid of revolution bounded by
rotated about the y-axis
13)(3)( 2 xxgandxxf
10 x
Practice 7-3 Shells
Reference
http://www.msstate.edu/dept/abelc/math/volume.html