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 Question from Patty, a student: On a step pyramid - do you count each side of the step as a face? - and each corner a vertex? - How do I find the volume of a step pyramid?

Hi Patty.

A "face" of a step pyramid is an exposed continuous 2 dimensional surface without corners.

There is one face on the top of the top brick or course. There are four more on the N, E, W, S faces of that top brick. The bottom of the top brick isn't exposed, so it isn't included. On the next level down, the tops are all continuous on the same surface as each other, so that's just one more. And that tier has four faces N, E, W, S as well.

So every tier contributes 5 faces to the pyramid.

As for the volume, let's call the top tier level L = 1 and the one below it level L = 2.
There are (1)2 level 1 bricks. So a one level step pyramid has (1)2 bricks.
There are (3)2 level 2 bricks. So a two level step pyramid has (1)2 + (3)2 bricks.
There are (5)2 level 3 bricks. So a three level step pyramid has (1)2 + (3)2 + (5)2 bricks.

Can you write an expression for the total bricks in an L-level step pyramid? That's the volume in bricks. See if you can simplify it.

Cheers,
Stephen La Rocque.

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