Clown Hats

Weekly Problem 51 - 2015
Charlie is making clown hats from a piece of cardboard. What is the maximum number he can make?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
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Problem



Charlie is making clown hats from a circular piece of cardboard.

Image
Clown Hats


The circumference of the base of each hat equals its slant height, which in turn is equal to the radius of the piece of cardboard. What is the maximum number of hats that Charlie can make from the piece of cardboard?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.