Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Gutter

Age 14 to 16
Challenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

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 ?

You may also like

Crossing the Bridge

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

The Fastest Cyclist

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo