Piece of Cake
'Work out how to calculate sector areas using intuition to solve this problem!'
Which piece of cake is the biggest? How can you compare the size of different parts of a circle if the circles don't all have the same radius? Print and cut the circles and put them in order of size! How can we justify our answers are correct?
Answers to these questions may lie within our natural intuition. In reasoning answers to this puzzle, we may find we are subconsciously deriving the formulae for the area of fractions of a circle!
Here are some photos of the pieces. Which is the biggest? (you can choose to view full screen in the bottom right hand corner once the slideshow has started)
Here follows an outline of what the task is.
- Print and cut out the shapes
- The challenge is to put them in order of size from smallest to largest
- Use reasoning to explain decisions
- Attempt to generalise about the formula for sector areas.