Volume of Pyramid
‘Make pyramid models and solve a puzzle to fit them together. Use this to find a formula for the volume.’
If you discover rules and formula for yourself then you’ll understand that mathematics is real and not abstract. If you take ownership of these formulae then they should have more meaning to you, and hopefully you’ll be more likely to remember them. The aim of this activity is for you to derive the formula for the volume of square based pyramid by constructing and producing a model and working with your classmates to put together a puzzle.
Resources & Description

Students will need some rough paper, a piece of thin card (approximately 25cm by 25cm), a pencil, a ruler and set square (optional), as well as scissors and sticky tape.

Students need to construct the net of a square based pyramid. Here are the instructions for the Pyramid Construction.

Working in groups, fit 6 pyramids together and use this to find the volume of one of the pyramids.

The formula for the volume of a square based pyramid can be derived using the following Deriving the Formula.

This document will provide an excellent summary for the students of the learning that has happened in this activity.

These plastic models can help students visualise the general rule. This square based pyramid has the same dimensions as the cube: the base area is the same and the height is the same. How are the volumes of these two 3D shapes related?
 If the models are not available in the classroom, the following video might help you to see

This cone has the same dimensions as the cylinder: the base area is the same and the height is the same. How are the volumes of these two 3D shapes related?

Here are some questions to put into practice what has be learned Volume of Pyramid Practice.

The solutions to the worksheet above can be found Volume of Pyramid Answers

There are some teacher notes available Pyramid Model TN