A puzzling pyramid 

Grade 9s challenged themselves today to calculate the volume and surface area of this container.

The container is not a rectangular prism.  The square base on the bottom is larger than the square  base on the top.  The following measurements were provided:  the side length of the bottom square was 12.5cm

The side length measured along the edge was 21cm

And the diagonals of the top square are 12cm

We worked hard and realized quickly that the pythagorean theorem would be important on several occasions!  We also needed to use our area of a trapezoid song!

Some groups noted similarities to a pyramid, but one that had been chopped.

We noticed that it was going to be hard to figure out the height of the pyramid.  The ribbon attached turned out to be a very lucky length!

We measured the ribbon (77cm) then worked on figuring out what we’d be able to figure out with that information.  We used string on the pyramid model to help us visualize our ideas.

We planned to calculate the volume of the large pyramid and subtract the volume of the small pyramid.  We used the pythagorean theorem again using half the ribbon length as an addition to the original height of the trapezoid which combined to make the total slant height of the pyramid.  

We learned that a cubic centimetre is a millilitre, and used that to convert our volume to litres.

We compared the container to known volumes (nalgene bottles, or 2L bottles of pop) to check for how reasonable our answers were.

One group tested their volume calculations by repeatedly filling  a 1L water bottle and dumping it into the container.  By doing this slowly, they determined that they had over estimated the capacity of the container, and would have had a big puddle on the floor if they had actually poured close to 3L into the container.  

Best quote of the day: “this math class is more fun than my music class!” 🙂