This activity comes from Julie Reulbach (Her blog is I Speak Math and her Twitter handle is @jreulbach). The URL link above will take you to her blog post about the activity summarized below. 

After students have learned the formula for the volume of a cylinder, you can build off that understanding to help them connect the volume of a cone to the volume of a cylinder.

Here’s the basic activity, as described on Julie’s blog:

1. I start by showing them a cylinder, and having a student write the volume formula on the board.  I have not asked them to memorize the volume formula of a cylinder, but after day 1, they all know it.  It’s magical.  I then pull a cone out of the cylinder and ask them what they notice/wonder.  They notice that the circle has the same circumference and the height is the same.  Excellent.  I then ask them what they wonder about the volume of the two objects.  Most groups decide that it is about 1/2, except for this group.
2. I then let them pour cheerios (or marshmallows) from the cone into the cylinder.  They notice it takes THREE cones to fill up the cylinder.  I have them talk with their table to adjust the [formula for the] volume of a cylinder.  Today, ALL of my students said, “Divide the volume of a cylinder by 3!” and one group even told me that was the same as multiplying by 1/3.
3. After I write their observations on the board, I show them the actual formulas from their Geometry Booklets¹ [HSE teachers can show students the formulas from the HSE Reference Sheet] and ask them to write down what they learned today on that page.  I think this is the most important part because I don’t want them to forget HOW they discovered the formula.  Today a student said, “We just invented already invented math!”

In the comments of her post, Julie describes (a) a different version of the activity where students create the cones themselves and (b) her method for constructing the cones for teachers to make their own.

“I believe we traced the circumference of the top and measured the height. Then used card stock. I remember wrapping it around in a cone and taping it. We also covered the paper in foil to make them more durable. They were not perfect, but close enough for kids to realize it was 1/3.”

As a final note, Julie writes:

 Please, please, please do discovery learning with your students.  It does take more time but will actually will save you more time in the end because you won’t have to re-teach it!

[1] To read more about beautiful Julie’s Geometry Booklets read her post – Student Made Geometry Booklets Improve Assessments – Creativity Strikes Again! It is a great way to make the definitions and formulas in geometry more engaging for our students.