Cylindrical Shells

Cylindrical Shells

1. V = 2pi*r*h

2. Height

   • One function
     • h = f(x)
   • 2 functions
     • h = top-bottom or right-left

3. Radius

   • Rotated about axis
     • x-axis : r=y
     • y-axis : r=x
   • About number (a)
     • Depends on where f(x) is in regards to the axis of rotation
       • EX: about y=3
         • dy
           • r = 3-y, if shell is is below y=3
             • think of it like "top - bottom"
       • Ex: about x=-2
         • dx
           • r = x-(-2) = x+2, if shell is to the right of y=-2
             • think of it like "right - left"
       • Ex: about y=1
         • dx
           • r = y-1, if shell is above y=1