'Explore cones by making one! A great puzzle that helps to understand the formulae for cones'
It sounds easy, but is it? Make a cone with a base radius of 10 cm and a perpendicular height of 24 cm. What needs to be considered, solved, calculated to make this possible? What does the net of a cone look like? How can we get the dimensions right? Cones are fascinating shapes in the category of those with a curved surface that begin to mess with our perception a little. This activity helps to explore the structure of cones and understand how we generate the formula for the area of the curved surface. So what starts out sounding like simple practical activity ends up as a good look at logical deduction and the mathematical holy grail of proof.
The problem is set out in the paragraph above but is broken down a little more in this Making Cones worksheet that can be printed and shared. There are some Making cones teacher's notes to help think about how to get the best out of this simple activity.
Below are some photos of the activity in action;
In addition to the worksheet, each group will need;
- A piece of A2 card from which to construct their cones,
- Some scissors,
- Some scrap paper,
- Some tape to stick the cones together.
Geometry of 3D solids.
New - Section 3.4, Previous - Section 5.5
Here follows an outline of the task
- Students are simply asked to accurately build a cone with the given dimensions.
- Students are told they only have the one piece of card and need to be sure to get their measurements right before they start cutting.
- Teacher will help groups and give hints and clues as appropriate.
- Once cones are made, students work on the second part of the task to generate formulae.
- Depending on the group and the progress, teacher may take the lead on the above.
- Students conclude with the formula for the surface area of a cone.