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An Unusual Shape

Age 11 to 14
Challenge Level Yellow starYellow star
Secondary curriculum
  • Problem
  • Getting Started
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An Unusual Shape printable sheet


Stuart tethered his goat to one end of a $20$-foot length of rope and attached the other end of the rope to a hook fixed to the side of his shed.

When he came back the goat had eaten all the grass within its reach.
Here is a picture showing the region eaten by the goat:

 

Where did Stuart fix the rope?

What was the area grazed by the goat?

Could the goat have eaten more grass if the rope had been attached to a different point on the shed? 

Experiment with different lengths of rope. Where should the hook be positioned each time to allow the goat to eat the maximum amount of grass?

 

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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.

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