Purpose

The purpose of this activity is for students to create open cylinders and calculate their volume. In doing so students consider the relative effects of increasing and decreasing height and radius on the volume.

Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.

Activity

By rolling A4 sized rectangles of paper you can make two different ‘open’ cylinders, like this:

Which of the two cylinders has the greatest volume?

What sized rectangle of paper will produce cylinders with the same volume when rolled in this way?

### The procedural approach (show more)

- The student makes each cylinder and calculates the volumes using measurements.

### The conceptual approach (show more)

- The student applies relationships among the radius, diameter, and circumference of a circle, between side lengths of standard paper sizes, and conversions between units of volume.