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## 'Cylinder Cutting' printed from http://nrich.maths.org/

This activity has been particularly
created for the most able. (The pupils that you come
across in many classrooms just once every few years.)

We start off with this tube (like one from inside a roll
of kitchen paper):

The tube has a seam running through it (that forms a helix)
.You'll have to carefully cut along that seam and then open it out
and flatten it a little.

Now you will notice a parallelogram. It will very easily return to
the original cylinder shape, BUT we can produce another cylinder by
putting the two shorter edges together.

Then you have a cylinder that looks more like this:

You are now encouraged to consider taking an $A4$ sheet of paper
and cutting it at an angle, in such a way that you can roll it up
to produce a similar cylinder (like the kitchen roll one). You then
repeat the same cutting as above and create the second cylinder by
rolling it up differently.

Examine the lengths and volumes of these two cylinders and
the areas of the paper pieces.

Try many different examples by cutting differently.

Is there a way of cutting the $A4$ sheet to produce a shape in
which both cylinders have the same volume?

Explore further the shaped pieces you've produced.