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.
This activity assumes the students have experience in the following areas:
The problem is sufficiently open ended to allow the students freedom of choice in their approach. It may be scaffolded with guidance that leads to a solution, and/or the students might be given the opportunity to solve the problem independently.
The example responses at the end of the resource give an indication of the kind of response to expect from students who approach the problem in particular ways.
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 following prompts illustrate how this activity can be structured around the phases of the Mathematics Investigation Cycle.
Introduce the problem. Allow students time to read it and discuss in pairs or small groups.
Discuss ideas about how to solve the problem. Emphasise that, in the planning phase, you want students to say how they would solve the problem, not to actually solve it.
Allow students time to work through their strategy and find a solution to the problem.
Allow students time to check their answers and then either have them pair share with other groups or ask for volunteers to share their solution with the class.
The student makes each cylinder and calculates the volumes using measurements.
Click on the image to enlarge it. Click again to close.
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.
Click on the image to enlarge it. Click again to close.
Cubic millimetres are awkward units for volume, so students may convert the measures to cubic centimetres.
Click on the image to enlarge it. Click again to close.
Algebra can also be used to prove that for the volumes of cylinders to be equal the length and width of the rectangle must be equal, i.e. the rectangle is a square.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/a4-cylinders at 8:53pm on the 26th February 2024