Finding the volume of solids using 3D printed models.

Students in AP Calculus and AP Calculus BC got to see and touch some 3D printed models of solids.  The region R bounded by two equations, represents the base of the solid. Students need to find the volume of the solid formed by this base and whose cross sections perpendicular to the x- axis are squares, triangles or trapezoids. Showing the slices, helped students to see a visual of the integral.

 

The image above also shows volume of a solid of revolution using the shell method.