Finding the volume of the intersection of two cylinders is a common calculus problem. The shape also plays a role in this old (for the internet!) video from Brooklyn tech that inspired me to get a 3d printer:

Today for a fun project to start the week I decided to share the shape with the boys and see what they thought about it. My younger son went first:

After playing on the computer I had him explore the printed version of the shape – make sure to stay to about 1:25 to hear where he thinks this shape might occur in “real life” ðŸ™‚

Next my older son played with the shape on the computer. He remembered seeing it before in a project from a month ago on the intersection of 3 cylinders:

Exploring 3 intersecting cylinders with 3d printing

Next he played with printed shape. I asked him to describe how he thought you’d be able to figure out that the shape was made out of squares – I thought his answer was pretty interesting. This question gets to the math ideas behind the calculus problem.

It is sort of fun for kids to see and play with shapes like this – no need to wait for calculus anymore to explore interesting shapes!