Category Archives: surface area

Powerful imagery using Geogebra

I absolutely love Geogebra, I use it in nearly every lesson to the extent that I’m not sure how I would teach certain topics without it!

I’ve written before about the power of starting from a blank sheet (angles in parallel lines, trigonometry, circle theorems), but recently I have found and used some excellent visualisations that other users have created and kindly uploaded. I feel like this aspect of Geogebra has improved considerably over the last couple of years in particular the search. I often have an idea in my head for what I want to show students and within a few seconds I have found exactly what I need by searching.  Using dynamic geometry that you can narrate to (or not) is so much better than just playing a YouTube video.  I try to think of points where I can ask “what will happen if…” type questions.

Here are my latest finds that I have used in class recently. Click on them to take you directly to the Geogebra. I’m sure this collection will be added to as I find more.

 

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Generalising Surface area

What is the surface area of a cube of side length 1?
If we then cut this cube in half, and throw one of the halves away, what is surface area of the remaining cuboid?
Repeat the process, cut the shape in half along the same plane. What pattern can you see?

Screen Shot 2017-07-09 at 16.59.12

What is the general formula for the surface of a cuboid of width 1, depth 1 and height h?

What is the general formula for a cuboid of width 1, depth d and height h?

What is the general formula for a cuboid of width w, depth d and height h?

What other 3D shapes can you find the general formula for the surface area? Try:

  • A tetrahedron, side length a
  • A square based pyramid, base length a, height, h
  • A cylinder radius r, length l