Copyright © University of Cambridge. All rights reserved.

'Gutter' printed from

Show menu

We are still waiting for some good student contributions on this problem but here are some thoughts to help you :

You could start with the three shape posibilities in this illustration :

First the triangle : suppose a length of say 20 cm was folded in the centre, for which angle would the cross-section area be greatest ? If the length had been 40 cm instead of 20 cm would that change your answer ?

Now the rectangle cross-section : maybe start with an overall length of 20 cm again and try different proportions of side length to base. What proportion created the largest area, was that a surprise or an expected result ?

Finally, for now, the arc : for a specified length, say 20 cm, you could curve it a lot or a little. If you curve it a lot you will have more of the full circle but it's a smaller circle. If you curve the material only a little you get less of a larger circle. A spreadsheet might help you find the best choice and ease the burden of calculation.

I hope you enjoy finding that result, if you didn't guess it. Now compare all three results : notice anything ? Can you account for that ?