Delta Math has incredible sets for seeing volume of cross-sections and solids of revolutions. If you instruct your students to click on “show solution“, they can pull a slider to see the region become a solid! For the cross-section set, it shows the shape (square, rectangle, or triangle) growing along the base. For the disks, it includes the radius with the 3D shape. The washer set shows the washer inside the 3D shape. There is also a matching set, where students can practice matching up the 2D region with a resulting 3D shape, and vice versa.
The five sets I use are in the image below. I have also included videos of the volumes being created when you drag the slider so you can see how cool it is! Delta Math is free for teachers!
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This is such a great tip! I used the DeltaMath 3D volume sets with my calculus students last term, and watching the slider turn the region into a solid made cross-sections finally click for them. It’s amazing how much a little interactivity helps with abstract ideas, and on a totally different note, while browsing the other day I stumbled across a free little browser game where you drive through Lagos traffic, and it gave my students a good laugh during a brain break.