Solids of revolution and by cross section.

1. Cylindrical Shells
cylinders

2. If the function below is revolved about the x-axis, find the volume of
the solid generated between ƒ, the x-axis, x = 0, and x = 2.

3. If the function below defines an area between ƒ, the x-axis, x = 0,
and x = 2. If the cross sections are semi-circles, find the volume of
the solid.
What would the volume be if the cross sections were squares?
equilateral triangles?

4. How would things be different if the
function is revolved about the y-axis?
source