Exploring 3 intersecting cylinders with 3d printing

Calculating the volume of 3 intersecting cylinders is a classic calculus problem.  The 3 cylinder problem caught my attention a few years ago when Patrick Honner shared this video about the 3d printing lab at his high school:

I wrote about my reaction to the video here:

Learning from 3D Printing

Today we used our 3d printer and the F3 program to explore the intersection of three cylinders. Here’s what they boys had to say when they saw the setup on the F3 program – my older son went first:

Here’s what my younger son had to say:

After the shape finished printing I had the boys talk about their thoughts when they had the shape in front of them. Here’s my older son’s thoughts:

And next my younger son:

Even though this is probably a better Calculus example, I loved being able to share the shape with the boys. It is fun to hear kids talk and wonder about fun shapes like this one.