Mix, Then Spray

Where should I stop filling?

Measurement: Volume of Cylinders and Cones

This is an attempt to better develop the question by splitting the problem into more than 3 acts, since I found it difficult to make the intended learning goal obvious enough through visuals.

Act 1, Scene 1 – Introduce The Problem

Act 1 is split into two very short videos. The first, simply shows an empty spray bottle:

Act 1, Scene 2 – Introduce The Problem

At this point, some discussion regarding where the problem may go could be initiated. In order to lead students down the right path, show the next short clip:

While the question might seem obvious to students at this point (i.e.: how much vinegar/water do you need), we are actually going down a slightly different path.

Act 2 – Reveal Some Information

Show this video:

Students now know that they must predict:

Where on the bottle should I stop filling with vinegar?

They can make this prediction by drawing a line on an image of the bottle.

Looking closer at the spray bottle, you’ll notice that it is a 3D composite figure consisting of a cylinder and a cone. You might want to consider asking students:

Will the amount of vinegar stop before reaching the top of the cylinder, after, or will it stop right on the dividing line between the cylinder and the cone?

Will The Vinegar Will Stop Below The Cylinder/Cone Dividing Line?

Will The Vinegar Will Stop Above The Cylinder/Cone Dividing Line?

After asking for students to determine what information they need to make their best prediction, you can show them this video:

Alternatively, you could show the following images:

Height of the spray bottle:

Act 2 Information - Height of the Spray Bottle

Height of the cylindrical portion of the spray bottle:

Act 2 Information - Height of the Cylinder Portion of the Spray Bottle

Diameter of the spray bottle:

Act 2 Information - Diameter of the Spray Bottle

Act 3 – Watch the Answer

Now, your students can see how close they came based on their prediction and their mathematically calculated prediction:


I haven’t tried this task out yet, so if you do, please share how it went in the comments. Any ways to make it better? Let me know!

Download The Task and Resources

Grab all the videos, images and resources by clicking download below:


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About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.


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