Volumes by Cylindrical Shells Rita Korsunsky

Formula for the volumes by Shells method For volume of a solid, add up all the volumes of each shell: radius dx f(x) = height

How to draw the radius and the height 1) Take a point on the curve 2) Draw the radius perpendicular to the axis of rotation 3) Drop a height from the point parallel to the axis of rotation

Example#1 dx radius 2x – x2 x height 2

Example#2 y dx radius y = x2 height 3 - x 3 y = x + 2 x

Example#3 2 height dy y radius 2y3 – y4

Example#4 R r Find points of intersection: Using Washers Method:

Example#4 Or using Shell’s Method:

The End