An Unusual Shape
Why do this problem?
This problem offers the opportunity to practise calculating areas of circles and fractions of a circle in the context of an optimisation task.
Possible approach
This printable worksheet may be useful: An Unusual Shape.
Start by showing the diagram from the problem, and ask learners to think on their own for a few moments about where the goat might have been tethered to yield the area shown.
Once learners have established where to fix the hook for maximum goat nutrition (!), move on to other lengths of rope. Suggest that pairs of learners work with different lengths of rope, and finish by sharing their findings with the rest of the class.
Key questions
What can you say about the radius of each part of a circle?
Possible support
The activity can be modelled by building the frame of the shed from multilink cubes, and learners could use string to work out the shapes of the regions that could be made available to the goat, when fixing the hook at different points.
Possible extension
What happens if the rope is longer than the sum of the sides of the shed?
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