Volumes, Calculus, and Cucumbers

My calculus students have always had a hard time visualizing three-dimensional objects. So, a couple of years ago, I started using cucumbers to help them understand the theory behind using integration to calculate the volume of rotated solids. Here’s a more detailed explanation of the activity.

Actually cutting the cucumbers into disks, measuring each disk’s volume, and adding them up to approximate the total volume is a great hands-on exercise that reinforces the concept of using an integral to add up lots and lots (an infinite number!) of disks to calculate the volume of an irregular solid. Plus, they always enjoy having a snack after all that brain work!